On a class of fixed points for set contractions on partial metric spaces with a digraph-Reference-Cited by-同舟云学术

On a class of fixed points for set contractions on partial metric spaces with a digraph

Published:2023 Issue:1 Volume:8 Page:1304-1328
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Nazir Talat¹,Ali Zakaria¹,Jogan Shahin Nosrat¹,Sen Manuel de la²

Affiliation:

1. Department of Mathematical Sciences, University of South Africa, Florida 0003, South Africa

2. Institute of Research and Development of Processes, University of the Basque Country, Leioa 48940, Bizkaia, Spain

Abstract

<abstract><p>We investigate the existence of fixed point problems on a partial metric space. The results obtained are for set contractions in the domain of sets and the pattern for the partial metric space is constructed on a directed graph. Essentially, our main strategy is to employ generalized $ \phi $-contractions in order to prove our results, where the fixed points are investigated with a graph structure. Moreover, we state and prove the well-posedness of fixed point based problems of the generalized $ \phi $-contractive operator in the framework of a partial metric space. We illustrate the main results in this manuscript by providing several examples.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference32 articles.

1. M. Abbas, M. R. Alfuraidan, A. R. Khan, T. Nazir, Fixed point results for set-contractions on metric spaces with a directed graph, Fixed Point Theory Appl., 2015 (2015), 14. https://doi.org/10.1186/s13663-015-0263-z

2. M. Abbas, M. R. Alfuraidan, T. Nazir, M. Rashed, Common fixed points of multivalued $F$-contractions on metric spaces with a directed graph, Carpathian J. Math., 32 (2016), 1–12.

3. M. Abbas, B. Ali, Fixed point of Suzuki-Zamfirescu hybrid contractions in partial metric spaces via partial Hausdorff metric, Fixed Point Theory Appl., 2013 (2013), 1–21. https://doi.org/10.1186/1687-1812-2013-21

4. M. Abbas, V. Parvaneh, A. Razani, Periodic points of $T$-Ciric generalized contraction mappings in ordered metric spaces, Georgian Math. J., 19 (2012), 597–610. https://doi.org/10.1515/gmj-2012-0036

5. S. M. A. Aleomraninejad, S. Rezapour, N. Shahzad, Some fixed point results on a metric space with a graph, Topol. Appl., 159 (2012), 659–663. https://doi.org/10.1016/j.topol.2011.10.013