A Common Fixed Point Theorem in Fuzzy Metric Spaces

Abstract

In the present paper, we prove a fixed point theorem in Fuzzy metric spaces through weak compatibility.

Some Fixed Point Theorems for pair mapping in Complex Valued b-Metric Space

“…In 2013 Rao et al [13] introduce the concept of complex valued b-metric space which was more general then the well known complex valued metric space. In sequal A.A. Mukheimer [11] obtained common fixed point result satisfying certain rational expression in complex valued b-metric space.…”

Existence of solution of Urysohn integral equation through generalized contractive mapping

“…After the establishment of complex valued metric spaces, Rao et al [15] introduced the complex valued b-metric spaces and then several authors have contributed with different concepts in these spaces. One can see in ( [1], [9]- [13], [16]- [21]).…”

“…Rao et al [15] introduced the notion of complex valued b-metric spaces as follows. For the routine definitions like convergent sequence, Cauchy sequence, complete complex valued b-metric space we refer [15]. Lemma 1.5.…”

“…Lemma 1.5. [15] Let (X, d) be a complex valued b-metric space and let {x n } be a sequence in X. Then {x n } converges to x if and only if |d(x n , x)| → 0 as n → ∞.…”

COMMON COUPLED FIXED POINTS FOR FOUR MAPS USING alpha-ADMISSIBLE FUNCTIONS IN COMPLEX VALUED b- METRIC SPACES

“…Lemma 1. ( [9]) Let (X, d) be a complex valued b-metric space and let {x n } be a sequence in X.Then {x n } converges to x if and only if |d(x n , x)| → 0 as n → ∞.…”