Document Type: Special Issue on Fixed Point Theory
Author
- M. E. Samei ^{} ^{}
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran
Abstract
In this paper, we shall establish some fixed point theorems for mappings with the contractive condition of integrable type on complete intuitionistic fuzzy metric spaces $(X, M,N,*,\lozenge)$. We also use Lebesgue-integrable mapping to obtain new results. Akram, Zafar, and Siddiqui introduced the notion of $A$-contraction mapping on metric space. In this paper by using the main idea of the work, we introduce the concept of $A$-fuzzy contractive mappings. Finally, we support our results by some examples.
Keywords
Main Subjects
[1] M. Akram, A. A. Siddiqui, A general class of contractions: A-contractions, Novi Sad J. Math. 38 (1) (2008), 25-33.
[2] R. Bianchini, Su un problema di S. Riech riguardante la teori dei punti fissi, Boll. Un. Math. Ital. 5 (1972), 103-108.
[3] A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29 (2002), 531-536.
[4] D. Dey, A. Ganguly, M. Saha, Fixed point theorems for mappings under general contractive condition of integral type, Bull. Math. Anal. Appl. 3 (1) (2011), 27-34.
[5] C. Di Bari, C. Vetro, A fixed point theorem for a family of mappings in a fuzzy metric space, Rend. Circ. Math. Palermo. 52 (2003), 315-321.
[6] V. Gregori, A. Sapena, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems. 125 (2002), 245-252.
[7] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71-76.
[8] H. Karayilan, M. Telci, Common fixed point theorem for contractive type mappings in fuzzy metric spaces, Rend. Circ. Mat. Palermo. 60 (2011), 145-152.
[9] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos. Solitons. Fractals. 22 (2004), 1039-1046.
[10] M. Rafi, M. S. M. Noorani, Fixed point theorem on intuitionistic fuzzy metric spaces, Iran. J. Fuzzy System. 3 (1) (2006), 23-29.
[11] S. Reich, Kannan’s fixed point theorem, Boll. Un. Math. Ital. 4 (1971), 1-11.
[12] B. E. Rhoades, Two fixed point theorems formappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 63 (2003), 4007-4013.
[13] B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 314-334.