Araştırma Makalesi
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Yıl 2018, , 15 - 44, 15.09.2018
https://doi.org/10.33205/cma.453034

Öz

Kaynakça

  • [1] H. Afshari, H. Aydi, E.Karapinar, Existence of Fixed Points of Set-Valued Mappings in b-Metric Spaces, East Asian mathematical journal , volume 32, issue 3, 2016, Pages 319 332,
  • [2] H. Afshari, H. Aydi and E. Karapinar, On generalized alpha-phi-geraghty contractions on b-metricspaces, Georgian Math. Journal,
  • [3] R. P. Agarwal, H. Alsulami, E.Karapınar and F.Khojasteh, Remarks on some recent fixed point results in quaternion-valued metric spaces, Abstract and Applied Analysis, (2014) Article Id: 171624
  • [4] U.Aksoy, E. Karapinar and I. M. Erhan, Fixed points of generalized alpha-admissible contractions on b-metric spaces with an application to boundary value problems,Journal of Nonlinear and Convex Analysis, (2016). Volume 17,Number 6, 1095-1108
  • [5] Ali and Kamran, On alpha*-phi-contractive multi-valued mappings, Fixed Point Theory and Appl. 2013 2013:137.
  • [6] M. U. Ali, T. Kamran, E. Karapinar, On (alpha-phi-xi)-contractive multi-valued mappings, Fixed Point Theory Appl., 2014, 2014:7
  • [7] H. Alsulami, S.Gulyaz, E. Karapinar, I. Erhan, An Ulam stability result on quasi-b-metric-like spaces, Open Mathematics, Volume 14, Issue 1 (Jan 2016) DOI 10.1515/math-2016-0097,
  • [8] H. Alsulami, S. Almezel, E. Karapinar, F. Khojasteh, A note on fixed point results in complex valued metric spaces, Journal of Inequalities and Applications, 2015, 2015:33
  • [9] H. H. Alsulami, E. Karapınar, F. Khojasteh, A. F. Roldán-López-de-Hierro, A proposal to the study of contractions in quasi-metric spaces, Discrete Dynamics in Nature and Society2014, Article ID 269286, 10 pages.
  • [10] H. H. Alsulami, E. Karapnar, V. Rakocevic Ciric Type Nonunique Fixed Point Theorems onb-Metric Spaces, Filomat 31:11 (2017), 3147-3156
  • [11] P. Amiri, S. Rezapour, N. Shahzad, Fixed points of generalized alpha-phi-contractions, Revista de laReal Academia de Ciencias Exactas, Fisicas y Naturales Serie A Mate.,
  • [12] H. Aydi, M-F. Bota, E. Karapınar and S. Mitrovic, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl. 2012, 2012:88.
  • [13] H. Aydi, M-F. Bota, E. Karapınar and S. Moradi, A common fixed point for weak phi-contractions on b-metric spaces, Fixed Point Theory, 13(2012), No 2, 337-346.
  • [14] H. Aydi, E. Karapınar, B.Samet, Fixed points for generalized (alpha-phi)-contractions on generalized metric spaces, Journal of Inequalities and Applications 2014, 2014:229
  • [15] I.A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal., Unianowsk Gos. Ped. Inst. 30(1989), 26-37.
  • [16] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3 (1922) 133–181.
  • [17] V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, Preprint no. 3(1993), 3-9.
  • [18] V. Berinde, Sequences of operators and fixed points in quasimetric spaces, Stud. Univ. ”Babes-Bolyai”, Math., 16(4)(1996), 23-27.
  • [19] V. Berinde, Contractii generalizatesi aplicatii, Editura Club Press 22, Baia Mare, 1997.
  • [20] N. Bilgili, E. Karapınar, A note on “Common fixed points for (alpha-phi,beta)-weakly contractive mappings in generalized metric spaces”, Fixed Point Theory Appl. 2013, 2013:287.
  • [21] R.M. Bianchini, M. Grandolfi, Transformazioni di tipo contracttivo generalizzato in uno spazio metrico, Atti Acad. Naz. Lincei, VII. Ser., Rend., Cl. Sci. Fis. Mat. Natur. 45 (1968), 212-216.
  • [22] M. F. Bota-Boriceanu, A. Petru¸ sel, Ulam-Hyers stability for operatorial equations, Analel Univ. Al. I. Cuza, Ia¸ si, 57(2011), 65-74.
  • [23] M.-F. Bota, E. Karapinar and O. Mlesnite, Ulam-Hyers stability results for fixed point problems via alpha-psi-contractive mapping in b-metric space, Abstract and Applied Analysis, 2013 Article Id: 825293
  • [24] M. Boriceanu, A. Petru¸ sel, I.A. Rus, Fixed point theorems for some multivalued generalized contractions in b-metric spaces, International Journal of Mathematics and Statistics, 6(2010), 65-76.
  • [25] M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, IJMM, Vol 4, 3(2009), 285-301.
  • [26] M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ. Babes-Bolyai, Mathematica, 3(2009), 3-14.
  • [27] M. Bota, Dynamical Aspects in the Theory of Multivalued Operators, Cluj University Press, 2010.
  • [28] N. Bourbaki, Topologie G´ en´ erale, Herman, Paris, 1974.
  • [29] J. Brzdek, J. Chudziak, and Z. Pales, A fixed point approach to stability of functional equations, Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 17, pp. 6728-6732, 2011.
  • [30] J. Brzdek and K. Ciepliski, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 18, pp. 6861-6867, 2011.
  • [31] J. Brzdek and K. Cieplinski, A fixed point theorem and the Hyers-Ulam stability in non-Archimedean spaces, Journal of Mathematical Analysis and Applications, vol. 400, no. 1, pp. 68-75, 2013.
  • [32] L.B. Ciric, On some maps with a nonunique fixed point. Publ. Inst. Math., 17, 52–58 (1974).
  • [33] S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1(1993), 5-11.
  • [34] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 46(1998), 263-276.
  • [35] T.Do^ senovic, M. Postolache and S. Radenovic, On multiplicative metric spaces: survey FixedPoint Theory and Applications20162016:92
  • [36] W.-S. Du, A note on cone metric fixed point theory and its equivalence Nonlinear Analysis72 (2010), no : 5, 2259-2261.
  • [37] M. Frechet Sur quelques points du calcul fonctionnel, Rendic. Circ. Mat. Palermo 22 (1906)1-74.
  • [38] S.Gupta and B. Ram, Non-unique fixed point theorems of Ciric type, (Hindi) VijnanaParishad Anusandhan Patrika 41( 4), 217–231(1998).
  • [39] F. Hausdorff. Mengenle hre . W. de Gruyter & Co. , 1927.
  • [40] J. Hasanzade Asl, Sh. Rezapour and N. Shahzad, On fixed points of alpha-phi- contractivemultifunctions, Fixed Point Theory and Applications, 2012(2012), doi:10.1186/1687-1812-2012-212.
  • [41] N.Hussain, J.R. Roshan, V. Parvaneh and M.Abbas, Common fixed point results for weakcontractive mappings in ordered b-dislocated metric spaces with applications Journal of In-equalities and Applications (2013) 2013:486
  • [42] N. Hussain, Z. Kadelburg, S. Radenovi´ c, and F.Al-Solamy, Comparison Functions and FixedPoint Results in Partial Metric Spaces, Abstract and Applied Analysis, vol. 2012, Article ID605781, 15 pages, 2012.
  • [43] J. Heinonen, Lectures on Analysis on Metric Spaces, Springer Berlin, 2001.
  • [44] D. H. Hyers, On the stability of the linear functional equation, Proceedings of the NationalAcademy of Sciences of the United States of America, vol. 27, no. 4, pp. 222-224, 1941.
  • [45] M. Jleli and B. Samet, Remarks on G-metric spaces and fixed point theorems, Fixed PointTheory Appl. 2012, 2012:210, 7 pages.
  • [46] E. Karapinar, H. Piri and H. AlSulami, Fixed Points of Generalized F-Suzuki Type Contrac-tion in Complete b-Metric Spaces,,” Discrete Dynamics in Nature and Society, 2015 (2015),Article ID 969726, 8 pages
  • [47] E. Karapinar, H.Piri and H.H. AlSulami, Fixed Points of Generalized F-Suzuki Type Con-traction in Complete b-Metric Spaces” Discrete Dynamics in Nature and Society, 2015 (2015),Article ID 969726, 8 pages
  • [48] E. Karapinar, A New Non-Unique Fixed Point Theorem, J. Appl. Funct. Anal. , 7 (2012),no:1-2, 92-97.
  • [49] E. Karapinar, Some Nonunique Fixed Point Theorems of Ciric type on Cone Metric Spaces,Abstr. Appl. Anal., vol. 2010, Article ID 123094, 14 pages (2010).
  • [50] E. Karapinar, H. Piri and H. AlSulami, Fixed Points of Generalized F-Suzuki Type Contrac-tion in Complete b-Metric Spaces, Discrete Dynamics in Nature and Society, 2015 (2015),Article ID 969726, 8 pages
  • [51] E. Karapınar, P. Kuman, P. Salimi, On alpha-phi-Meri-Keeler contractive mappings, Fixed PointTheory Appl. 2013:94 (2013)
  • [52] E. Karapınar, H.H. Alsulami and M. Noorwali, Some extensions for Geragthy type contractivemappings Journal of Inequalities and Applications 2015:303 (2015)
  • [53] E. Karapınar, B.Samet, Generalized alpha-phi-Contractive Type Mappings and Related FixedPoint Theorems with Applications Abstract and Applied Analysis Volume 2012, Article ID793486, 17 pages
  • [54] E. Karapinar and W.-S. Du, A note on b-cone metric and its related results: Generalizationsor equivalence? , Fixed Point Theory and Applications, (2013), 2013:210
  • [55] F. Khojasteh, S. Shukla, S. Radenovi´ c, A new approach to the study of fixed point theoremsvia simulation functions, Filomat 29:6 (2015), 1189–1194.
  • [56] M.A. Kutbi , E. Karapinar, J. Ahmed, A. Azam, Some fixed point results for multi-valuedmappings in b-metric spaces , Journal of Inequalities and Applications 2014, 2014:126
  • [57] A. Latif, M. E. Gordji, E. Karapınar, W. Sintunavarat, Fixed point results for generalized(alpha-phi)-Meir-Keeler contractive mappings and applications, J. Ineq. Appl. 2014, 2014:68.
  • [58] V. La Rosa, P. Vetro, Common fixed points for ?-?-?-contractions in generalized metricspaces, Nonlinear Anal. Model. Control 19 (2014), no. 1, 43-54
  • [59] V. L. Laz^ ar, Ulam-Hyers stability for partial differential inclusions, Electronic Journal ofQualitative Theory of Differential Equations, 21 (2012), 1-19.
  • [60] Liu, Z. Q.: On Ciric type mappings with a nonunique coincidence points, Mathematica (Cluj)35(58),no. 2, 221–225(1993).
  • [61] Liu, Z., Guo, Z., Kang, S. M., Lee, S. K.: On Ciric type mappings with nonunique fixed andperiodic points, Int. J. Pure Appl. Math., 26(3),399–408 (2006).
  • [62] B. Mohammadi, S. Rezapour, N Shahzad, Some results on fixed points of alpha-phi-Ciric general-ized multifunctions. Fixed Point Theory Appl., 2013 2013:24 doi:10.1186/1687-1812-2013-24.
  • [63] J.J. Nieto, R. Rodr´ıguez-López, Contractive Mapping Theorems in Partially Ordered Setsand Applications to Ordinary Differential Equations, Order. 22 (2005) 223–239.
  • [64] B. G. Pachpatte, On Ciric type maps with a nonunique fixed point, Indian J. Pure Appl.Math., 10( 8), 1039–1043 (1979).
  • [65] M. Pacurar, A fixed point result for varphi-contractions on b-metric spaces without the bound-edness assumption, Fasc. Math., 43(2010), 127-137.
  • [66] T. P. Petru, A. Petrusel and J.-C. Yao, Ulam-Hyers stability for operatorial equations andinclusions via nonself operators, Taiwanese Journal of Mathematics, Vol. 15, No. 5, pp.2195-2212, October 2011.
  • [67] O. Popescu, Some new fixed point theorems for alpha-Geraghty-contraction type maps in metricspaces, Fixed Point Theory Appl. 2014, 2014:190
  • [68] A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and someapplications to matrix equations, Proc. Amer. Math. Soc. 132 (2003) 1435–1443.
  • [69] I. A. Rus, The theory of a metrical fixed point theorem: theoretical and applicative relevances,Fixed Point Theory, 9(2008), No. 2, 541-559.
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A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces

Yıl 2018, , 15 - 44, 15.09.2018
https://doi.org/10.33205/cma.453034

Öz

The aim of this short survey is to collect and combine basic notions and results in the fixed point theory in the context of $b$-metric spaces. It is also aimed to show that there are still enough rooms for several researchers in this interesting direction and a huge application potential.

Kaynakça

  • [1] H. Afshari, H. Aydi, E.Karapinar, Existence of Fixed Points of Set-Valued Mappings in b-Metric Spaces, East Asian mathematical journal , volume 32, issue 3, 2016, Pages 319 332,
  • [2] H. Afshari, H. Aydi and E. Karapinar, On generalized alpha-phi-geraghty contractions on b-metricspaces, Georgian Math. Journal,
  • [3] R. P. Agarwal, H. Alsulami, E.Karapınar and F.Khojasteh, Remarks on some recent fixed point results in quaternion-valued metric spaces, Abstract and Applied Analysis, (2014) Article Id: 171624
  • [4] U.Aksoy, E. Karapinar and I. M. Erhan, Fixed points of generalized alpha-admissible contractions on b-metric spaces with an application to boundary value problems,Journal of Nonlinear and Convex Analysis, (2016). Volume 17,Number 6, 1095-1108
  • [5] Ali and Kamran, On alpha*-phi-contractive multi-valued mappings, Fixed Point Theory and Appl. 2013 2013:137.
  • [6] M. U. Ali, T. Kamran, E. Karapinar, On (alpha-phi-xi)-contractive multi-valued mappings, Fixed Point Theory Appl., 2014, 2014:7
  • [7] H. Alsulami, S.Gulyaz, E. Karapinar, I. Erhan, An Ulam stability result on quasi-b-metric-like spaces, Open Mathematics, Volume 14, Issue 1 (Jan 2016) DOI 10.1515/math-2016-0097,
  • [8] H. Alsulami, S. Almezel, E. Karapinar, F. Khojasteh, A note on fixed point results in complex valued metric spaces, Journal of Inequalities and Applications, 2015, 2015:33
  • [9] H. H. Alsulami, E. Karapınar, F. Khojasteh, A. F. Roldán-López-de-Hierro, A proposal to the study of contractions in quasi-metric spaces, Discrete Dynamics in Nature and Society2014, Article ID 269286, 10 pages.
  • [10] H. H. Alsulami, E. Karapnar, V. Rakocevic Ciric Type Nonunique Fixed Point Theorems onb-Metric Spaces, Filomat 31:11 (2017), 3147-3156
  • [11] P. Amiri, S. Rezapour, N. Shahzad, Fixed points of generalized alpha-phi-contractions, Revista de laReal Academia de Ciencias Exactas, Fisicas y Naturales Serie A Mate.,
  • [12] H. Aydi, M-F. Bota, E. Karapınar and S. Mitrovic, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl. 2012, 2012:88.
  • [13] H. Aydi, M-F. Bota, E. Karapınar and S. Moradi, A common fixed point for weak phi-contractions on b-metric spaces, Fixed Point Theory, 13(2012), No 2, 337-346.
  • [14] H. Aydi, E. Karapınar, B.Samet, Fixed points for generalized (alpha-phi)-contractions on generalized metric spaces, Journal of Inequalities and Applications 2014, 2014:229
  • [15] I.A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal., Unianowsk Gos. Ped. Inst. 30(1989), 26-37.
  • [16] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3 (1922) 133–181.
  • [17] V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, Preprint no. 3(1993), 3-9.
  • [18] V. Berinde, Sequences of operators and fixed points in quasimetric spaces, Stud. Univ. ”Babes-Bolyai”, Math., 16(4)(1996), 23-27.
  • [19] V. Berinde, Contractii generalizatesi aplicatii, Editura Club Press 22, Baia Mare, 1997.
  • [20] N. Bilgili, E. Karapınar, A note on “Common fixed points for (alpha-phi,beta)-weakly contractive mappings in generalized metric spaces”, Fixed Point Theory Appl. 2013, 2013:287.
  • [21] R.M. Bianchini, M. Grandolfi, Transformazioni di tipo contracttivo generalizzato in uno spazio metrico, Atti Acad. Naz. Lincei, VII. Ser., Rend., Cl. Sci. Fis. Mat. Natur. 45 (1968), 212-216.
  • [22] M. F. Bota-Boriceanu, A. Petru¸ sel, Ulam-Hyers stability for operatorial equations, Analel Univ. Al. I. Cuza, Ia¸ si, 57(2011), 65-74.
  • [23] M.-F. Bota, E. Karapinar and O. Mlesnite, Ulam-Hyers stability results for fixed point problems via alpha-psi-contractive mapping in b-metric space, Abstract and Applied Analysis, 2013 Article Id: 825293
  • [24] M. Boriceanu, A. Petru¸ sel, I.A. Rus, Fixed point theorems for some multivalued generalized contractions in b-metric spaces, International Journal of Mathematics and Statistics, 6(2010), 65-76.
  • [25] M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, IJMM, Vol 4, 3(2009), 285-301.
  • [26] M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ. Babes-Bolyai, Mathematica, 3(2009), 3-14.
  • [27] M. Bota, Dynamical Aspects in the Theory of Multivalued Operators, Cluj University Press, 2010.
  • [28] N. Bourbaki, Topologie G´ en´ erale, Herman, Paris, 1974.
  • [29] J. Brzdek, J. Chudziak, and Z. Pales, A fixed point approach to stability of functional equations, Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 17, pp. 6728-6732, 2011.
  • [30] J. Brzdek and K. Ciepliski, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 18, pp. 6861-6867, 2011.
  • [31] J. Brzdek and K. Cieplinski, A fixed point theorem and the Hyers-Ulam stability in non-Archimedean spaces, Journal of Mathematical Analysis and Applications, vol. 400, no. 1, pp. 68-75, 2013.
  • [32] L.B. Ciric, On some maps with a nonunique fixed point. Publ. Inst. Math., 17, 52–58 (1974).
  • [33] S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1(1993), 5-11.
  • [34] S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 46(1998), 263-276.
  • [35] T.Do^ senovic, M. Postolache and S. Radenovic, On multiplicative metric spaces: survey FixedPoint Theory and Applications20162016:92
  • [36] W.-S. Du, A note on cone metric fixed point theory and its equivalence Nonlinear Analysis72 (2010), no : 5, 2259-2261.
  • [37] M. Frechet Sur quelques points du calcul fonctionnel, Rendic. Circ. Mat. Palermo 22 (1906)1-74.
  • [38] S.Gupta and B. Ram, Non-unique fixed point theorems of Ciric type, (Hindi) VijnanaParishad Anusandhan Patrika 41( 4), 217–231(1998).
  • [39] F. Hausdorff. Mengenle hre . W. de Gruyter & Co. , 1927.
  • [40] J. Hasanzade Asl, Sh. Rezapour and N. Shahzad, On fixed points of alpha-phi- contractivemultifunctions, Fixed Point Theory and Applications, 2012(2012), doi:10.1186/1687-1812-2012-212.
  • [41] N.Hussain, J.R. Roshan, V. Parvaneh and M.Abbas, Common fixed point results for weakcontractive mappings in ordered b-dislocated metric spaces with applications Journal of In-equalities and Applications (2013) 2013:486
  • [42] N. Hussain, Z. Kadelburg, S. Radenovi´ c, and F.Al-Solamy, Comparison Functions and FixedPoint Results in Partial Metric Spaces, Abstract and Applied Analysis, vol. 2012, Article ID605781, 15 pages, 2012.
  • [43] J. Heinonen, Lectures on Analysis on Metric Spaces, Springer Berlin, 2001.
  • [44] D. H. Hyers, On the stability of the linear functional equation, Proceedings of the NationalAcademy of Sciences of the United States of America, vol. 27, no. 4, pp. 222-224, 1941.
  • [45] M. Jleli and B. Samet, Remarks on G-metric spaces and fixed point theorems, Fixed PointTheory Appl. 2012, 2012:210, 7 pages.
  • [46] E. Karapinar, H. Piri and H. AlSulami, Fixed Points of Generalized F-Suzuki Type Contrac-tion in Complete b-Metric Spaces,,” Discrete Dynamics in Nature and Society, 2015 (2015),Article ID 969726, 8 pages
  • [47] E. Karapinar, H.Piri and H.H. AlSulami, Fixed Points of Generalized F-Suzuki Type Con-traction in Complete b-Metric Spaces” Discrete Dynamics in Nature and Society, 2015 (2015),Article ID 969726, 8 pages
  • [48] E. Karapinar, A New Non-Unique Fixed Point Theorem, J. Appl. Funct. Anal. , 7 (2012),no:1-2, 92-97.
  • [49] E. Karapinar, Some Nonunique Fixed Point Theorems of Ciric type on Cone Metric Spaces,Abstr. Appl. Anal., vol. 2010, Article ID 123094, 14 pages (2010).
  • [50] E. Karapinar, H. Piri and H. AlSulami, Fixed Points of Generalized F-Suzuki Type Contrac-tion in Complete b-Metric Spaces, Discrete Dynamics in Nature and Society, 2015 (2015),Article ID 969726, 8 pages
  • [51] E. Karapınar, P. Kuman, P. Salimi, On alpha-phi-Meri-Keeler contractive mappings, Fixed PointTheory Appl. 2013:94 (2013)
  • [52] E. Karapınar, H.H. Alsulami and M. Noorwali, Some extensions for Geragthy type contractivemappings Journal of Inequalities and Applications 2015:303 (2015)
  • [53] E. Karapınar, B.Samet, Generalized alpha-phi-Contractive Type Mappings and Related FixedPoint Theorems with Applications Abstract and Applied Analysis Volume 2012, Article ID793486, 17 pages
  • [54] E. Karapinar and W.-S. Du, A note on b-cone metric and its related results: Generalizationsor equivalence? , Fixed Point Theory and Applications, (2013), 2013:210
  • [55] F. Khojasteh, S. Shukla, S. Radenovi´ c, A new approach to the study of fixed point theoremsvia simulation functions, Filomat 29:6 (2015), 1189–1194.
  • [56] M.A. Kutbi , E. Karapinar, J. Ahmed, A. Azam, Some fixed point results for multi-valuedmappings in b-metric spaces , Journal of Inequalities and Applications 2014, 2014:126
  • [57] A. Latif, M. E. Gordji, E. Karapınar, W. Sintunavarat, Fixed point results for generalized(alpha-phi)-Meir-Keeler contractive mappings and applications, J. Ineq. Appl. 2014, 2014:68.
  • [58] V. La Rosa, P. Vetro, Common fixed points for ?-?-?-contractions in generalized metricspaces, Nonlinear Anal. Model. Control 19 (2014), no. 1, 43-54
  • [59] V. L. Laz^ ar, Ulam-Hyers stability for partial differential inclusions, Electronic Journal ofQualitative Theory of Differential Equations, 21 (2012), 1-19.
  • [60] Liu, Z. Q.: On Ciric type mappings with a nonunique coincidence points, Mathematica (Cluj)35(58),no. 2, 221–225(1993).
  • [61] Liu, Z., Guo, Z., Kang, S. M., Lee, S. K.: On Ciric type mappings with nonunique fixed andperiodic points, Int. J. Pure Appl. Math., 26(3),399–408 (2006).
  • [62] B. Mohammadi, S. Rezapour, N Shahzad, Some results on fixed points of alpha-phi-Ciric general-ized multifunctions. Fixed Point Theory Appl., 2013 2013:24 doi:10.1186/1687-1812-2013-24.
  • [63] J.J. Nieto, R. Rodr´ıguez-López, Contractive Mapping Theorems in Partially Ordered Setsand Applications to Ordinary Differential Equations, Order. 22 (2005) 223–239.
  • [64] B. G. Pachpatte, On Ciric type maps with a nonunique fixed point, Indian J. Pure Appl.Math., 10( 8), 1039–1043 (1979).
  • [65] M. Pacurar, A fixed point result for varphi-contractions on b-metric spaces without the bound-edness assumption, Fasc. Math., 43(2010), 127-137.
  • [66] T. P. Petru, A. Petrusel and J.-C. Yao, Ulam-Hyers stability for operatorial equations andinclusions via nonself operators, Taiwanese Journal of Mathematics, Vol. 15, No. 5, pp.2195-2212, October 2011.
  • [67] O. Popescu, Some new fixed point theorems for alpha-Geraghty-contraction type maps in metricspaces, Fixed Point Theory Appl. 2014, 2014:190
  • [68] A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and someapplications to matrix equations, Proc. Amer. Math. Soc. 132 (2003) 1435–1443.
  • [69] I. A. Rus, The theory of a metrical fixed point theorem: theoretical and applicative relevances,Fixed Point Theory, 9(2008), No. 2, 541-559.
  • [70] I. A. Rus, Generalized contractions and applications, Cluj University Press, Cluj-Napoca,2001.
  • [71] I. A. Rus, Remarks on Ulam stability of the operatorial equations, Fixed Point Theory,10(2009), No. 2, 305-320.
  • [72] I. A. Rus, A. Petru¸ sel, A. Sˆınt^ am^ arian, Data dependence of the fixed points set of somemultivalued weakly Picard operators, Nonlinear Anal. 52(2003), 1947-1959.
  • [73] P. Salimi, A. Latif, N. Hussain, Modified alpha-phi-contractive mappings with applications, FixedPoint Theory Appl., 2013 2013:151 doi:10.1186/1687-1812-2013-151.
  • [74] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for alpha-phi-contractive type mappings, Non-linear Analysis 75 (2012), 2154-2165.
  • [75] B. Samet, C.Vetro, and F.Vetro , Remarks on G-Metric Spaces, International Journal ofAnalysis, Volume 2013 (2013), Article ID 917158, 6 pages
  • [76] S. Shukla, Partial b-Metric Spaces and Fixed Point Theorems, Mediterr. J. Math. 11 (2014),703711
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Toplam 80 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Erdal Karapınar

Yayımlanma Tarihi 15 Eylül 2018
Yayımlandığı Sayı Yıl 2018

Kaynak Göster

APA Karapınar, E. (2018). A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces. Constructive Mathematical Analysis, 1(1), 15-44. https://doi.org/10.33205/cma.453034
AMA Karapınar E. A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces. CMA. Eylül 2018;1(1):15-44. doi:10.33205/cma.453034
Chicago Karapınar, Erdal. “A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces”. Constructive Mathematical Analysis 1, sy. 1 (Eylül 2018): 15-44. https://doi.org/10.33205/cma.453034.
EndNote Karapınar E (01 Eylül 2018) A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces. Constructive Mathematical Analysis 1 1 15–44.
IEEE E. Karapınar, “A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces”, CMA, c. 1, sy. 1, ss. 15–44, 2018, doi: 10.33205/cma.453034.
ISNAD Karapınar, Erdal. “A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces”. Constructive Mathematical Analysis 1/1 (Eylül 2018), 15-44. https://doi.org/10.33205/cma.453034.
JAMA Karapınar E. A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces. CMA. 2018;1:15–44.
MLA Karapınar, Erdal. “A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces”. Constructive Mathematical Analysis, c. 1, sy. 1, 2018, ss. 15-44, doi:10.33205/cma.453034.
Vancouver Karapınar E. A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces. CMA. 2018;1(1):15-44.

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