<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The concept of generalized convex contraction was introduced and studied by V. Istrăţescu and the notion of <italic>b</italic>-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 <italic>b</italic>-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 <italic>b</italic>-metric spaces.</p></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.

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

Faculty of Mathematics and Computer Science

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

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

Published Online: Dec 29, 2017

Page range: 119 - 142

Received: Apr 26, 2017

Accepted: Oct 26, 2017

DOI: https://doi.org/10.1515/awutm-2017-0018

Keywords
iterated function systems consisting of generalized convex contractions, -metric spaces, fixed points

© 2017 Flavian Georgescu, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Dec 29, 2017

Page range: 119 - 142

Received: Apr 26, 2017

Accepted: Oct 26, 2017

DOI: https://doi.org/10.1515/awutm-2017-0018

Keywordsiterated function systems consisting of generalized convex contractions, -metric spaces, fixed points

© 2017 Flavian Georgescu, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
iterated function systems consisting of generalized convex contractions, -metric spaces, fixed points