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Year 2021, Volume: 9 Issue: 1, 24 - 32, 28.04.2021

Nihal Taş , Nihal Özgür

Abstract

References

  • [1] A. Aghajani, M. Abbas and J.R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces, Filomat 28 (6) (2014), 1087-1101.
  • [2] A. Aghajani, M. Abbas and J.R. Roshan, Common fixed point of generalized weak contractive appings in partially ordered b-metric spaces, Math. Slovaca 64 (4) (2014), 941-960.
  • [3] T. Van An, N. Van Dung and V.T. Le Hang, A new approach to fixed point theorems on G-metric spaces, Topology Appl. 160 (12) (2013), 1486-1493.
  • [4] A.H. Ansari, O. Ege and S. Radenovic, Some fixed point results on complex valued Gb-metric spaces, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM 112 (2) (2018), 463-472.
  • [5] I.A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. 30 (1989), 26-37.
  • [6] N. Van Dung, N.T. Hieu and S. Radojevic, Fixed point theorems for g-monotone maps on partially ordered S-metric spaces, Filomat 28 (9) (2014), 1885-1898.
  • [7] O. Ege, Complex valued Gb-metric spaces, J. Comput. Anal. Appl. 21 (2) (2016), 363-368.
  • [8] O. Ege, Some fixed point theorems in complex valued Gb-metric spaces, J. Nonlinear Convex Anal. 18 (11) (2017), 1997-2005.
  • [9] O. Ege and I. Karaca, Common fixed point results on complex valued Gb-metric spaces, Thai J. Math. 16 (3) (2018), 775-787.
  • [10] O. Ege, C. Park and A.H. Ansari, A different approach to complex valued Gb-metric spaces, Adv. Differ. Equ. 2020 (2020), 152.
  • [11] N.T. Hieu, N.T. Thanh Ly and N. Van Dung, A generalization of Ciric quasi-contractions for maps on S-metric spaces, Thai J. Math. 13 (2) (2015), 369-380.
  • [12] N. Hussain, V. Parvaneh and F. Golkarmanesh, Coupled and tripled coincidence point results under (F; g)-invariant sets in Gb-metric spaces and G-a-admissible mappings, Math. Sci. 9 (2015), 11-26.
  • [13] N. Mlaiki, A. Mukheimer, Y. Rohen, N. Souayah and T. Abdeljawad, Fixed point theorems for a-Ya -Y-contractive mapping in Sb-metric spaces, J. Math. Anal. 8 (5) (2017), 40-46.
  • [14] N. Mlaiki, Extended Sb-metric spaces, J. Math. Anal. 9 (1) (2018), 124-135.
  • [15] S.K. Mohanta, Some fixed point theorems in G-metric spaces, An. S¸tiint¸. Univ. ”Ovidius” Constant¸a Ser. Mat. 20 (1) (2012), 285-305.
  • [16] A. Mukheimer, Extended partial Sb-metric spaces, Axioms, 7 (4) (2018), 87.
  • [17] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2) (2006), 289-297.
  • [18] N.Y. Ozgur and N. Tas, Some fixed point theorems on S-metric spaces, Mat. Vesnik 69 (1) (2017), 39-52.
  • [19] N.Y. Ozgur and N. Tas, Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25), Math. Sci. 11 (1) (2017), 7-16.
  • [20] N.Y. Ozgur and N. Tas, Some generalizations of fixed point theorems on S-metric spaces, Essays in Mathematics and Its Applications in Honor of Vladimir Arnold, New York, Springer, 2016.
  • [21] N.Y. Ozgur¨ and N. Tas¸, Common fixed point results on complex-valued S-metric spaces, Sahand Commun. Math. Anal. (17) (2) (2019), 83-105.
  • [22] N.Y. Ozgur and N. Tas¸, The Picard theorem on S-metric spaces, Acta Math. Sci. Ser. B (Engl. Ed.) 38 (4) (2018), 1245-1258.
  • [23] S. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik 64 (3) (2012), 258-266.
  • [24] S. Sedghi and N. Van Dung, Fixed point theorems on S-metric spaces, Mat. Vesnik 66 (1) (2014), 113-124.
  • [25] S. Sedghi, N. Shobkolaei, J.R. Roshan and W. Shatanawi, Coupled fixed point theorems in Gb-metric spaces, Mat. Vesnik 66 (2) (2014), 190-201.
  • [26] S. Sedghi, A. Gholidahneh, T. Dosenoviˇc,´ J. Esfahani and S. Radenovic,´ Common fixed point of four maps in Sb-metric spaces, J. Linear Topol. Algebra 5 (2) (2016), 93-104.
  • [27] N. Souayah, A fixed point in partial Sb-metric spaces, An. S¸tiint¸. Univ. ”Ovidius” Constant¸a Ser. Mat. 24 (3) (2016), 351-362.
  • [28] N. Souayah and N. Mlaiki, A fixed point theorem in Sb-metric space, J. Math. Computer Sci. 16 (2016), 131-139.
  • [29] M. Ughade, D. Turkoglu, S.K. Singh and R.D. Daheriya, Some fixed point theorems in Ab-metric space, British Journal of Mathematics & Computer Science 19 (6) (2016), 1-24.
  • [30] J. Vujakovic, G.N.V. Kishore, K.P.R. Rao, S. Radenovic and S. Sadik, Existence and unique coupled solution in Sb-metric spaces by rational contraction with application, Mathematics, 7 (4) (2019), 313.

New Generalized Fixed Point Results on $S_{b}$-Metric Spaces

Year 2021, Volume: 9 Issue: 1, 24 - 32, 28.04.2021

Nihal Taş , Nihal Özgür

Abstract

Recently $S_{b}$-metric spaces have been introduced as the generalizations of metric and $S$-metric spaces. In this paper, we generalize the classical Banach's contraction principle using the theory of a complete $S_{b}$-metric space. Also, we give an application to linear equation systems using the $S_{b}$-metric generated by a metric.

Keywords

$S_{b}$-metric space fixed point Banach's contraction principle linear equation

References

  • [1] A. Aghajani, M. Abbas and J.R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered Gb-metric spaces, Filomat 28 (6) (2014), 1087-1101.
  • [2] A. Aghajani, M. Abbas and J.R. Roshan, Common fixed point of generalized weak contractive appings in partially ordered b-metric spaces, Math. Slovaca 64 (4) (2014), 941-960.
  • [3] T. Van An, N. Van Dung and V.T. Le Hang, A new approach to fixed point theorems on G-metric spaces, Topology Appl. 160 (12) (2013), 1486-1493.
  • [4] A.H. Ansari, O. Ege and S. Radenovic, Some fixed point results on complex valued Gb-metric spaces, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A Mat. RACSAM 112 (2) (2018), 463-472.
  • [5] I.A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst. 30 (1989), 26-37.
  • [6] N. Van Dung, N.T. Hieu and S. Radojevic, Fixed point theorems for g-monotone maps on partially ordered S-metric spaces, Filomat 28 (9) (2014), 1885-1898.
  • [7] O. Ege, Complex valued Gb-metric spaces, J. Comput. Anal. Appl. 21 (2) (2016), 363-368.
  • [8] O. Ege, Some fixed point theorems in complex valued Gb-metric spaces, J. Nonlinear Convex Anal. 18 (11) (2017), 1997-2005.
  • [9] O. Ege and I. Karaca, Common fixed point results on complex valued Gb-metric spaces, Thai J. Math. 16 (3) (2018), 775-787.
  • [10] O. Ege, C. Park and A.H. Ansari, A different approach to complex valued Gb-metric spaces, Adv. Differ. Equ. 2020 (2020), 152.
  • [11] N.T. Hieu, N.T. Thanh Ly and N. Van Dung, A generalization of Ciric quasi-contractions for maps on S-metric spaces, Thai J. Math. 13 (2) (2015), 369-380.
  • [12] N. Hussain, V. Parvaneh and F. Golkarmanesh, Coupled and tripled coincidence point results under (F; g)-invariant sets in Gb-metric spaces and G-a-admissible mappings, Math. Sci. 9 (2015), 11-26.
  • [13] N. Mlaiki, A. Mukheimer, Y. Rohen, N. Souayah and T. Abdeljawad, Fixed point theorems for a-Ya -Y-contractive mapping in Sb-metric spaces, J. Math. Anal. 8 (5) (2017), 40-46.
  • [14] N. Mlaiki, Extended Sb-metric spaces, J. Math. Anal. 9 (1) (2018), 124-135.
  • [15] S.K. Mohanta, Some fixed point theorems in G-metric spaces, An. S¸tiint¸. Univ. ”Ovidius” Constant¸a Ser. Mat. 20 (1) (2012), 285-305.
  • [16] A. Mukheimer, Extended partial Sb-metric spaces, Axioms, 7 (4) (2018), 87.
  • [17] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2) (2006), 289-297.
  • [18] N.Y. Ozgur and N. Tas, Some fixed point theorems on S-metric spaces, Mat. Vesnik 69 (1) (2017), 39-52.
  • [19] N.Y. Ozgur and N. Tas, Some new contractive mappings on S-metric spaces and their relationships with the mapping (S25), Math. Sci. 11 (1) (2017), 7-16.
  • [20] N.Y. Ozgur and N. Tas, Some generalizations of fixed point theorems on S-metric spaces, Essays in Mathematics and Its Applications in Honor of Vladimir Arnold, New York, Springer, 2016.
  • [21] N.Y. Ozgur¨ and N. Tas¸, Common fixed point results on complex-valued S-metric spaces, Sahand Commun. Math. Anal. (17) (2) (2019), 83-105.
  • [22] N.Y. Ozgur and N. Tas¸, The Picard theorem on S-metric spaces, Acta Math. Sci. Ser. B (Engl. Ed.) 38 (4) (2018), 1245-1258.
  • [23] S. Sedghi, N. Shobe and A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik 64 (3) (2012), 258-266.
  • [24] S. Sedghi and N. Van Dung, Fixed point theorems on S-metric spaces, Mat. Vesnik 66 (1) (2014), 113-124.
  • [25] S. Sedghi, N. Shobkolaei, J.R. Roshan and W. Shatanawi, Coupled fixed point theorems in Gb-metric spaces, Mat. Vesnik 66 (2) (2014), 190-201.
  • [26] S. Sedghi, A. Gholidahneh, T. Dosenoviˇc,´ J. Esfahani and S. Radenovic,´ Common fixed point of four maps in Sb-metric spaces, J. Linear Topol. Algebra 5 (2) (2016), 93-104.
  • [27] N. Souayah, A fixed point in partial Sb-metric spaces, An. S¸tiint¸. Univ. ”Ovidius” Constant¸a Ser. Mat. 24 (3) (2016), 351-362.
  • [28] N. Souayah and N. Mlaiki, A fixed point theorem in Sb-metric space, J. Math. Computer Sci. 16 (2016), 131-139.
  • [29] M. Ughade, D. Turkoglu, S.K. Singh and R.D. Daheriya, Some fixed point theorems in Ab-metric space, British Journal of Mathematics & Computer Science 19 (6) (2016), 1-24.
  • [30] J. Vujakovic, G.N.V. Kishore, K.P.R. Rao, S. Radenovic and S. Sadik, Existence and unique coupled solution in Sb-metric spaces by rational contraction with application, Mathematics, 7 (4) (2019), 313.
There are 30 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Nihal Taş

Nihal Özgür

Publication Date April 28, 2021
Submission Date March 10, 2020
Acceptance Date March 17, 2021
Published in Issue Year 2021 Volume: 9 Issue: 1

Cite

APA Taş, N., & Özgür, N. (2021). New Generalized Fixed Point Results on $S_{b}$-Metric Spaces. Konuralp Journal of Mathematics, 9(1), 24-32.
AMA Taş N, Özgür N. New Generalized Fixed Point Results on $S_{b}$-Metric Spaces. Konuralp J. Math. April 2021;9(1):24-32.
Chicago Taş, Nihal, and Nihal Özgür. “New Generalized Fixed Point Results on $S_{b}$-Metric Spaces”. Konuralp Journal of Mathematics 9, no. 1 (April 2021): 24-32.
EndNote Taş N, Özgür N (April 1, 2021) New Generalized Fixed Point Results on $S_{b}$-Metric Spaces. Konuralp Journal of Mathematics 9 1 24–32.
IEEE N. Taş and N. Özgür, “New Generalized Fixed Point Results on $S_{b}$-Metric Spaces”, Konuralp J. Math., vol. 9, no. 1, pp. 24–32, 2021.
ISNAD Taş, Nihal - Özgür, Nihal. “New Generalized Fixed Point Results on $S_{b}$-Metric Spaces”. Konuralp Journal of Mathematics 9/1 (April 2021), 24-32.
JAMA Taş N, Özgür N. New Generalized Fixed Point Results on $S_{b}$-Metric Spaces. Konuralp J. Math. 2021;9:24–32.
MLA Taş, Nihal and Nihal Özgür. “New Generalized Fixed Point Results on $S_{b}$-Metric Spaces”. Konuralp Journal of Mathematics, vol. 9, no. 1, 2021, pp. 24-32.
Vancouver Taş N, Özgür N. New Generalized Fixed Point Results on $S_{b}$-Metric Spaces. Konuralp J. Math. 2021;9(1):24-32.
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