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On some fixed point theorems for ordered vectorial Ćirić-Prešić type contractions

On some fixed point theorems for ordered vectorial Ćirić-Prešić type contractions Banach contraction mapping principle is one of the building blocks of metric fixed point theory. Numerous generalizations of this principle have been made usually by altering the metric space with a more general space and changing the contraction conditions. In this paper, by utilizing these ways we present a fixed point theorem for ordered vectorial Ćirić-Preš ić type contractions. This result extends many results in the literature such as the ones obtained for Ćirić-Prešić type contractions on both metric and partially ordered metric spaces. With some remarks, we emphasize that every ordered Prešić and ordered Ćirić-Pre šić type contractions has to be an ordered vectorial Ćirić -Prešić type contraction nevertheless the converse may not be true in general. In addition, with an example, we support our conclusion and also show that the results existing in the literature are not applicable to this example. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

On some fixed point theorems for ordered vectorial Ćirić-Prešić type contractions

The Journal of Analysis , Volume OnlineFirst – Sep 26, 2022

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to The Forum D’Analystes 2022. Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0971-3611
eISSN
2367-2501
DOI
10.1007/s41478-022-00504-z
Publisher site
See Article on Publisher Site

Abstract

Banach contraction mapping principle is one of the building blocks of metric fixed point theory. Numerous generalizations of this principle have been made usually by altering the metric space with a more general space and changing the contraction conditions. In this paper, by utilizing these ways we present a fixed point theorem for ordered vectorial Ćirić-Preš ić type contractions. This result extends many results in the literature such as the ones obtained for Ćirić-Prešić type contractions on both metric and partially ordered metric spaces. With some remarks, we emphasize that every ordered Prešić and ordered Ćirić-Pre šić type contractions has to be an ordered vectorial Ćirić -Prešić type contraction nevertheless the converse may not be true in general. In addition, with an example, we support our conclusion and also show that the results existing in the literature are not applicable to this example.

Journal

The Journal of AnalysisSpringer Journals

Published: Sep 26, 2022

Keywords: Ćirić–Prešić type operators; Fixed point; Riesz space; Partial ordered metric spaces; Ordered vector metric spaces; 46A19; 46A40; 47B60; 47H10; 54H25

References