Fixed point theorem for mappings satisfying contractive condition of integral type on intuitionistic fuzzy metric space

Subject Areas : Fixed point theory

M. E. Samei ¹

1 - Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran

Received: 2018-02-12 Accepted : 2018-04-18 Published : 2018-09-01

Keywords: fixed point, Intuitionistic fuzzy metric space, $A$-fuzzy contractions,

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.

References:

[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.