Title: Fixed point results of Altman integral type mapping in S-metric spaces
Author(s): Mujeeb Ur Rahman, Muhammad Sarwar, Muhib Ur Rahman
Pages: 58-63
Cite as:
Mujeeb Ur Rahman, Muhammad Sarwar, Muhib Ur Rahman, Fixed point results of Altman integral type mapping in S-metric spaces, Int. J. Anal. Appl., 10 (1) (2016), 58-63.

Abstract


In this article, we introduce the concept of ϕ-weakly commuting self-mappings pairs in $S$-metric space. Using this idea we establish a common fixed point theorem of Altman integral type for four self-mappings in the context of $S$-metric space. Example is constructed to support our result.

Full Text: PDF

 

References


  1. M. Altman, A fixed point theorem in compact metric spaces, American Mathematical Monthly, 82(1975), 827-829.

  2. A. Garbone and S.P. Singh, Common fixed point theorem for Altman type mapping, Indian Journal of Pure and Applied Mathematics, 18(1987), 1082-1087.

  3. Y. Li and F. Gu, Common fixed point theorem of Altman integral type mapping, The Journal of N0nlinear Sciences and Applications, 2(2009), 214-218.

  4. Z. Mustafa and B. Sims, A new approach to generalized metric spaces, Journal of Non-Linear Convex Analysis, 7(2006), 289-297.

  5. F. Gu and H. Ye, Common fixed point theorem of Altman integral type mapping in G-metric spaces, Abstract and Applied Analysis, 2012(2012) Article ID 630457.

  6. S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorem in S-metric spaces, Matema. Bech., 64(2012), 258-266.

  7. S. Sedghi and V.N. Dung, Fixed point theorems on S-metric spaces, Matema. Bech., 66(2014), 113-124.

  8. G. Jungck, Compatible mappings and common fixed points, International Journal of Mathematics and Mathematical Sciences, 9(1986), 771-779.

  9. G. Jungck, Common fixed points for non-continuous non-self mappings on non-metric spaces, Far East Journal of Mathematical Sciences, 4(1996), 199-212.

  10. M. Sarwar and M.U. Rahman, Six maps version for Hardy-Rogers type mapping in dislocated metric space, Proceeding of A. Razmadze Mathematical Institute, 166(2014), 121-132.

  11. M.U. Rahman and M. Sarwar, A fixed point theorem for three pairs of mappings satisfying contractive condition of integral type in dislocated metric space, Journal of Operetors, 2014 (2014), Article ID 750427.

  12. A. Branciari, A fixed point theorem for mappings satisfying general contractive condition of integral type, International Journal of Mathematics and Mathematical Sciences, 29(2002), 531-536.