Some Common Fixed Point Theorems in Generalized Vector Metric Spaces

Main Article Content

Rajesh Shrivastava, Rajendra Kumar Dubey, Pankaj Tiwari

Abstract

In this paper we give some theorems on point of coincidence and common fixed point for two self mappings satisfying some general contractive conditions in generalized vector spaces. Our results generalize some well-known recent results in this direction.

Article Details

References

  1. C.D. Aliprantis, K.C. Border, ”Infinite Dimensional Analysis”, Springer-Verlag, Derlin, 1999.
  2. C.D. Aliprantis and R. Tourky, Cones and Duality, in: Graduate studies in Mathematics, Amer. Math. Soc. 84 (2007). 215-240.
  3. Beg, M. Abbas and T. Nazir, Generalized cone metric spaces, J. Nonlinear Sci. Appl. 3 (2010), no. 1, 23-31.
  4. L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 322 (2007), 1468-1476.
  5. Meir and E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl. 28 (1969), 326-329.
  6. Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear and Convex Anal. 7 (2006), no. 2, 289-297.
  7. Z. Mustafa, W. Shatanawi and M. Bataineh, Existence of fixed point result in G-metric spaces, , Int. J. Math. Math. Sci. 2009(2009), page 10, Article ID 283028.
  8. Z. Mustafa and B. Sims, Fixed point theorems for contractive mappings in complete G-metric space, Fixed Point Theory Appl. 2009(2009), page 10, Article ID 917175.
  9. Z. Mustafa, H. Obiedat and F. Awawdeh, Some of fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl., 2008(2008), Article ID 189870,page 12.
  10. W. Shatanawi: Some fixed point theorems in ordered G-metric spaces and applications, Abstr. Appl. Anal.,(2011), Article ID 126205, 11 p.
  11. W. Shatanawi, Fixed point theory for contractive mappings satisfying - maps in G-metric spaces, Fixed Point Theory Appl. 2010(2010), Article ID 181650, 9 pages.
  12. M. Abbas, T. Nazir and P. Vetro: Common fixed point results for three maps in G-metric spaces, Filomat, 25(2011), 1-17.
  13. H. Aydi: A fixed point result involving a generalized weakly contractive condition in G-metric spaces, Bull. Math. Anal. Appl., 3(2011), No. 4, 180-188.