Abstract
Our purpose in this paper is to extend the fixed point results of a ψ F -contraction introduced by Secelean N.A. and Wardowski D. ( ψ F -Contractions: Not Necessarily Nonexpansive Picard Operators, Results. Math.70(3), 415–431 (2016)) defined on a metric space X into itself to the case of mapping defined on the product space X I , where I is a set of positive integers (natural numbers). Some improvements to the conditions imposed on function F and space X are provided. An illustrative example is given.
Highlights
As it is well known, Banach contraction principle is of crucial importance in fixed point theory with many applications in various fields of mathematics
Secelean considers F-contractions defined on the product space X I with values in X, where I is a set of positive integers, and proved two fixed point theorems for such mappings
In this paper we generalize the fixed point result given in [3] for ψF-contractions defined on complete metric space X by extending this mappings on product metric space X I endowed with the sup metric, where I is a set of positive integers
Summary
As it is well known, Banach contraction principle is of crucial importance in fixed point theory with many applications in various fields of mathematics. There is a sustained endeavor of many researchers obtain new classes of Picard mappings by extend and improve the survey of F-contractions by generalizing the function F and the spaces with metric type structures. In this respect, in [2] N.A. Secelean considers F-contractions defined on the product space X I with values in X, where I is a set of positive integers, and proved two fixed point theorems for such mappings.
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