Abstract
We establish three major fixed-point theorems for functions satisfying generalized rational type almost contraction conditions. Firstly we consider the case of a single mapping, secondly we look at the case of a triplet of mappings and we conclude by the case of a family of mappings. The theorems we present generalize similar results already obtained by Abbas, Rhoades, Gaba, and others. The operators we consider are all of the weakly Picard type.
Highlights
Introduction and preliminariesRecently, applications of G-metric spaces, in the fields like optimization theory, differential and integral equations, have been discovered and this has generated a lot of interest for these type of spaces
We prove three main fixed point results in that setting
We propose generalizations which ensure existence results for fixed points, and to this goal we investigate the character of the sequence of iterates {Tnx}∞n=0 (resp. {Ti(xi−1)}∞i=0 ) where T:X → X
Summary
Received: 03 December 2017 Accepted: 20 February 2018 First Published: 07 March 2018
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