Startseite Relation theoretic contractions and their applications in b-metric like spaces
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Relation theoretic contractions and their applications in b-metric like spaces

  • Anita Tomar ORCID logo EMAIL logo , Meena Joshi ORCID logo und S. K. Padaliya
Veröffentlicht/Copyright: 28. Januar 2022

Abstract

We introduce a relational generalized Meir–Keeler contraction and a relational generalized Meir–Keeler contraction with rational terms in non-complete relational b-metric like spaces in order to establish non-unique fixed point results for a discontinuous single-valued map. Also, we provide an illustrative example to demonstrate that a relational generalized Meir–Keeler contraction with rational terms in a relational b-metric like space admits discontinuity at the fixed point. Thereby, we provide a novel explanation via a binary relation to the question of the existence of a contractive map admitting a fixed point at the point of discontinuity. Finally, we give applications to solve an initial value problem and a non-linear matrix equation which demonstrate the usability and effectiveness of our results.

MSC 2010: 47H10; 54H25; 46L05

Acknowledgements

The authors are grateful to the anonymous referees for their precise remarks and suggestions which led to the improvement of this paper.

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Received: 2020-02-08
Revised: 2021-02-21
Accepted: 2021-05-01
Published Online: 2022-01-28
Published in Print: 2022-12-01

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