Fixed Point Results for Contraction Mappings in G_b- Cone Metric Spaces

Manoj Ughade, R.D. Daheriya
1.455 543

Abstract


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

Keywords


G_b- cone metric spaces; normal cones; non-normal cones; contraction; fixed points.

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References


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).