Iterated Function Systems Consisting of Generalized Convex Contractions in the Framework of Complete Strong b-metric Spaces

Flavian Georgescu

doi:10.1515/awutm-2017-0018

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Iterated Function Systems Consisting of Generalized Convex Contractions in the Framework of Complete Strong b-metric Spaces

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 55 (2017): Issue 2 (December 2017)

By: Flavian Georgescu

Open Access

|Dec 2017

Abstract

The concept of generalized convex contraction was introduced and studied by V. Istrăţescu and the notion of b-metric space was introduced by I. A. Bakhtin and S. Czerwik. In this paper we combine these two elements by studying iterated function systems consisting of generalized convex contractions on the framework of b-metric spaces. More precisely we prove the existence and uniqueness of the attractor of such a system providing in this way a generalization of Istrăţescu’s convex contractions fixed point theorem in the setting of complete strong b-metric spaces.

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