Title: Cyclic Contraction on S- Metric Space
Author(s): Animesh Gupta
Pages: 119-130
Cite as:
Animesh Gupta, Cyclic Contraction on S- Metric Space, Int. J. Anal. Appl., 3 (2) (2013), 119-130.

Abstract


In this paper we introduced the concepts of cyclic contraction on S- metric space and proved some fixed point theorems on S- metric space. Our presented results are proper generalization of Sedghi et al. [14]. We also give an example in support of our theorem.

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References


  1. R. Chugh, T. Kadian, A. Rani, B.E. Rhoades, Property P in G-metric spaces, Fixed Point Theory Appl. Vol. 2010, Article ID 401684. Google Scholar

  2. B.C. Dhage, Generalized metric spaces mappings with fixed point, Bull. Calcutta Math. Soc. 84 (1992), 329-336. Google Scholar

  3. S. Gahler, 2-metrische Raume und iher topoloische Struktur, Math. Nachr. 26 (1963), 115- 148. Google Scholar

  4. Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006), 289C297. Google Scholar

  5. Z. Mustafa, H. Obiedat, F. Awawdeh, Some common fixed point theorems for mapping on complete G-metric spaces, Fixed Point Theory Appl. Vol. 2008, Article ID 189870. Google Scholar

  6. 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. Google Scholar

  7. Z. Mustafa, B. Sims, Some results concerning D-metric spaces, Proc. Internat. Conf. Fixed Point Theory and Applications, pp. 189-198, Valencia, Spain, 2003. Google Scholar

  8. S.V.R. Naidu , K.P.R. Rao, N. Srinivasa Rao, On the topology of D-metric spaces and the generation of D-metric spaces from metric spaces, Internat. J. Math. Math. Sci. 2004 (2004), No. 51, 2719-2740. Google Scholar

  9. S.V.R. Naidu, K.P.R. Rao, N. Srinivasa Rao, On the concepts of balls in a D-metric space, Internat. J. Math. Math. Sci. 2005 (2005), 133-141. Google Scholar

  10. S.V.R. Naidu, K.P.R. Rao, N. Srinivasa Rao, On convergent sequences and fixed point theorems in D-metric spaces, Internat. J. Math. Math. Sci. 2005 (2005), 1969-1988. Google Scholar

  11. S. Sedghi, K.P.R. Rao, N. Shobe, Common fixed point theorems for six weakly compatible mappings in D∗-metric spaces, Internat. J. Math. Math. Sci. 6 (2007), 225-237. Google Scholar

  12. S. Sedghi, N. Shobe, H. Zhou, A common fixed point theorem in D∗-metric spaces, Fixed Point Theory Appl. Vol. 2007, Article ID 27906, 13 pages. Google Scholar

  13. W. Shatanawi, Fixed point theory for contractive mappings satisfying ψ-maps in G-metric spaces, Fixed Point Theory Appl. Vol. 2010, Article ID 181650. Google Scholar

  14. S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorem in S-metric spaces,Mat. Vesnik 64 (2012), 258-266. Google Scholar