Abstract
In this paper we prove the existence and uniqueness of couple fixed point theorems for three mappings satisfying some new rational contractive conditions. We prove our results in the frame work of Gb-metric space which is recently introduced by Aghajani et al. (Filomat 28(6):1087–1101, 2014). Illustrative example is also given to support our result.
Highlights
Introduction and preliminariesA metric space is a set X together with a function d which assigns a real number d(x, y) to every pair x, y belonging to X satisfying the properties: 1. d(x, y) ≥ 0 and d(x, y) = 0 iff x = y 2. d(x, y) = d(y, x), 3. d(x, y) + d(y, z) ≥ d(x, z).The pair (X, d) is called a metric space
Since the introduction of metric space by Frachet, there is a lot of generalisation of this space
In our present study we prove some unique coupled common fixed point theorems for three mappings satisfying some new rational contractive conditions in Gb-metric space
Summary
After a gap of about twenty years Bhaskar and Lakshmikantham (2006) in the year 2006 proved a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order. In our present study we prove some unique coupled common fixed point theorems for three mappings satisfying some new rational contractive conditions in Gb-metric space. Definition 1 (Mustafa et al 2013b) Let X be a nonempty set and G : X3 → R+ be a function satisfying the following properties: 1.
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