Abstract
Abstract We prove some coincidence and common fixed point results for three mappings satisfying a generalized weak contractive condition in ordered partial metric spaces. As application of the presented results, we give a unique fixed point result for a mapping satisfying a weak cyclical contractive condition. We also provide some illustrative examples. MSC:47H10, 54H25.
Highlights
1 Introduction and preliminaries In the last decades, several authors have worked on domain theory in order to equip semantics domain with a notion of distance
Yi is a cyclic representation of Inspired by Karapinar [ ] and Gopal et al [ ], we present the notion of a cyclic weak (ψ, φ)-contraction in partial metric spaces
Tunisia. 2Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi 34, Palermo, 90123, Italy. 3Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, 10140, Thailand
Summary
We claim that {Rxn} is a Cauchy sequence in the partial metric space (X, p) To this aim, we distinguish the following two cases. We deduce that {Rxn} is a Cauchy sequence in the partial metric space (X, p), which is complete, so {Rxn} converges to some u ∈ X, that is, from (p ) and Definition . Remains true without assuming the continuity of T, S and R, and the partial-compatibility of the pairs {T, R} and {R, S} This is the purpose of the theorem. We obtain the following common fixed point result involving two mappings. Let X = [ , ] be endowed with the partial metric p(x, y) = max{x, y} and the order given as follows: Consider the mappings
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