Yıl 2015,
Cilt: 28 Sayı: 4, 659 - 673, 22.03.2015
Manoj Ughade
,
R.d. Daheriya
Kaynakça
- B. C. Dhage, “Generalized metric space and mapping with fixed point,” Bulletin of Calcutta Mathematical Society, vol. 84, pp. 329–336, 1992.
- B. C. Dhage, “On generalized metric spaces and topological structure. II,” Pure and Applied Mathematika Sciences, vol. 40, no. 1-2, pp. 37–41, 1994.
- B. C. Dhage, “A common fixed point principle in D-metric spaces,” Bulletin of the Calcutta Mathematical Society, vol. 91, no. 6, pp. 475–480, 1999.
- B. C. Dhage “Generalized metric spaces and topological structure. I,” Annalele Stintificeale Universitatii Al.I. Cuza, vol. 46, no. 1, pp. 3–24, 2000.
- Z. Mustafa and B. Sims, “Some remarks concerning D-metric spaces,” in Proceedings of the International Conference on Fixed Point Theory and Applications, pp. 189–198, Yokohama, Japan, 2004.
- Z. Mustafa and B. Sims, “A new approach to generalized metric spaces,” Journal of Nonlinear and Convex Analysis, vol. 7, no. 2, pp. 289–297, 2006.
- M. Abbas and B. E. Rhoades, “Common fixed point results for non commuting mappings without continuity in generalized metric spaces,” Applied Mathematics and Computation, vol. 215, no. 1, pp. 262–269, 2009.
- H. Aydi, W. Shatanawi, and C. Vetro, “On generalized weakly G-contraction mapping in G-metric spaces,” Computers & Mathematics with Applications, vol. 62, pp. 4222–4229, 2011.
- H. Aydi, “A fixed point result involving a generalized weakly contractive condition in G-metric spaces,” Bulletin of Mathematical Analysis and Applications, vol. 3, no. 4, pp. 180–188, 2011.
- H. Aydi, “A common fixed point of integral type contraction in generalized metric spaces,” Journal of Advanced Mathematical Studies, vol. 5, no. 1, pp. 111–117, 2012.
- Z. Mustafa, A new structure for generalized metric spaces with applications to fixed point theory, Ph.D. thesis, The University of Newcastle, Callaghan, Australia, 2005.
- Z. Mustafa, H. Obiedat, and F. Awawdeh, “Some fixed point theorem for mapping on complete G-metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 189870, 12 pages, 2008.
- Z. Mustafa and B. Sims, “Fixed point theorems for contractive mappings in complete G-metric spaces,” Fixed Point Theory and Applications, vol. 2009, Article ID 917175, 10 pages, 2009.
- Z. Mustafa, W. Shatanawi, and M. Bataineh, “Existence of fixed point results in G-metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 2009, Article ID 283028, 10 pages, 2009.
- R. Saadati, S. M. Vaezpour, P. Vetro, and B. E. Rhoades, “Fixed point theorems in generalized partially ordered G-metric spaces,” Mathematical and Computer Modeling, vol. 52, no. 5-6, pp. 797–801, 2010.
- W. Shatanawi, “Fixed point theory for contractive mappings satisfying Φ-maps in G-metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 181650, 9 pages, 2010.
- W. Shatanawi, “Some fixed point theorems in ordered G-metric spaces and applications,” Abstract and Applied Analysis, vol. 2011, Article ID 126205, 11 pages, 2011.
- K. P. Chi, “On a fixed point theorem for certain class of maps satisfying a contractive condition depended on another function,” Labachevskii journal of mathematics, vol.30, no. 4, pp. 289-291, 2009.
- K. P. Chi and H. T. Thuy, “A fixed point theorem in 2-metric spaces for certain class of maps that satisfy a contractive condition dependent on an another function,” Labachevskii journal of mathematics, vol.31, no. 4, pp. 338-346, 2010.
- Duran Turkoglu and Nurcan Bilgili, Some fixed point theorem for mapping on complete G-cone metric spaces, Journal of Applied Functional Analysis, Vol.7, No’s 1-2,118-137.
- Asadollah Aghajani, Mujahid Abbas, Jamal Rezaei Roshan, Common Fixed Point of Generalized Weak Contractive Mappings in Partially Ordered G_b-metric Spaces, Filomat 28:6 (2014), 1087–1101 DOI 10.2298/FIL140 6087A.
- Beg, I, Abbas, M, Nazir, T: Generalized cone metric spaces. J. Nonlinear Sci. Appl. 3(1), 21-31 (2010).
- Moore, RE, Cloud, MJ: Computational Functional Analysis, 2nd edn. Ellis Horwood Series in Mathematics and Its Applications. Woodhead Publishing, Cambridge (2007).
- Noor, A: Principles of Variational Inequalities. Lambert Academic Publishing, Saarbrucken (2009).
- Abbas, M, Hussain, N, Rhoades, BE: Coincidence point theorems for multivalued f -weak contraction mappings and applications. RACSAM Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. a Mat. 105(2), 261-272 (2011).
- Azam, A, Arshad, M, Beg, I: Existence of fixed points in complete cone metric spaces. Int. J. Mod. Math. 5(1), 91-99 (2010).
Fixed Point and Common Fixed Point Results for Contraction Mappings in Gb - Cone Metric Spaces
Yıl 2015,
Cilt: 28 Sayı: 4, 659 - 673, 22.03.2015
Manoj Ughade
,
R.d. Daheriya
Öz
The intent of this paper is to introduce the concept of G_b-cone metric space and we give some properties about this space. Further, we establish some fixed point theorems in -cone metric spaces. Moreover, some examples are provided to illustrate the usability of the obtained results
Kaynakça
- B. C. Dhage, “Generalized metric space and mapping with fixed point,” Bulletin of Calcutta Mathematical Society, vol. 84, pp. 329–336, 1992.
- B. C. Dhage, “On generalized metric spaces and topological structure. II,” Pure and Applied Mathematika Sciences, vol. 40, no. 1-2, pp. 37–41, 1994.
- B. C. Dhage, “A common fixed point principle in D-metric spaces,” Bulletin of the Calcutta Mathematical Society, vol. 91, no. 6, pp. 475–480, 1999.
- B. C. Dhage “Generalized metric spaces and topological structure. I,” Annalele Stintificeale Universitatii Al.I. Cuza, vol. 46, no. 1, pp. 3–24, 2000.
- Z. Mustafa and B. Sims, “Some remarks concerning D-metric spaces,” in Proceedings of the International Conference on Fixed Point Theory and Applications, pp. 189–198, Yokohama, Japan, 2004.
- Z. Mustafa and B. Sims, “A new approach to generalized metric spaces,” Journal of Nonlinear and Convex Analysis, vol. 7, no. 2, pp. 289–297, 2006.
- M. Abbas and B. E. Rhoades, “Common fixed point results for non commuting mappings without continuity in generalized metric spaces,” Applied Mathematics and Computation, vol. 215, no. 1, pp. 262–269, 2009.
- H. Aydi, W. Shatanawi, and C. Vetro, “On generalized weakly G-contraction mapping in G-metric spaces,” Computers & Mathematics with Applications, vol. 62, pp. 4222–4229, 2011.
- H. Aydi, “A fixed point result involving a generalized weakly contractive condition in G-metric spaces,” Bulletin of Mathematical Analysis and Applications, vol. 3, no. 4, pp. 180–188, 2011.
- H. Aydi, “A common fixed point of integral type contraction in generalized metric spaces,” Journal of Advanced Mathematical Studies, vol. 5, no. 1, pp. 111–117, 2012.
- Z. Mustafa, A new structure for generalized metric spaces with applications to fixed point theory, Ph.D. thesis, The University of Newcastle, Callaghan, Australia, 2005.
- Z. Mustafa, H. Obiedat, and F. Awawdeh, “Some fixed point theorem for mapping on complete G-metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 189870, 12 pages, 2008.
- Z. Mustafa and B. Sims, “Fixed point theorems for contractive mappings in complete G-metric spaces,” Fixed Point Theory and Applications, vol. 2009, Article ID 917175, 10 pages, 2009.
- Z. Mustafa, W. Shatanawi, and M. Bataineh, “Existence of fixed point results in G-metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 2009, Article ID 283028, 10 pages, 2009.
- R. Saadati, S. M. Vaezpour, P. Vetro, and B. E. Rhoades, “Fixed point theorems in generalized partially ordered G-metric spaces,” Mathematical and Computer Modeling, vol. 52, no. 5-6, pp. 797–801, 2010.
- W. Shatanawi, “Fixed point theory for contractive mappings satisfying Φ-maps in G-metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 181650, 9 pages, 2010.
- W. Shatanawi, “Some fixed point theorems in ordered G-metric spaces and applications,” Abstract and Applied Analysis, vol. 2011, Article ID 126205, 11 pages, 2011.
- K. P. Chi, “On a fixed point theorem for certain class of maps satisfying a contractive condition depended on another function,” Labachevskii journal of mathematics, vol.30, no. 4, pp. 289-291, 2009.
- K. P. Chi and H. T. Thuy, “A fixed point theorem in 2-metric spaces for certain class of maps that satisfy a contractive condition dependent on an another function,” Labachevskii journal of mathematics, vol.31, no. 4, pp. 338-346, 2010.
- Duran Turkoglu and Nurcan Bilgili, Some fixed point theorem for mapping on complete G-cone metric spaces, Journal of Applied Functional Analysis, Vol.7, No’s 1-2,118-137.
- Asadollah Aghajani, Mujahid Abbas, Jamal Rezaei Roshan, Common Fixed Point of Generalized Weak Contractive Mappings in Partially Ordered G_b-metric Spaces, Filomat 28:6 (2014), 1087–1101 DOI 10.2298/FIL140 6087A.
- Beg, I, Abbas, M, Nazir, T: Generalized cone metric spaces. J. Nonlinear Sci. Appl. 3(1), 21-31 (2010).
- Moore, RE, Cloud, MJ: Computational Functional Analysis, 2nd edn. Ellis Horwood Series in Mathematics and Its Applications. Woodhead Publishing, Cambridge (2007).
- Noor, A: Principles of Variational Inequalities. Lambert Academic Publishing, Saarbrucken (2009).
- Abbas, M, Hussain, N, Rhoades, BE: Coincidence point theorems for multivalued f -weak contraction mappings and applications. RACSAM Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. a Mat. 105(2), 261-272 (2011).
- Azam, A, Arshad, M, Beg, I: Existence of fixed points in complete cone metric spaces. Int. J. Mod. Math. 5(1), 91-99 (2010).