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Research Article | Open Access

Existence fixed-point theorems in the partial b-metric spaces and an application to the boundary value problem

Saeed Anwar1, Muhammad Nazam2( ), Hamed H Al Sulami3, Aftab Hussain3, Khalil Javed1, Muhammad Arshad1
Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan
Department of Mathematics, Allama Iqbal Open University, Islamabad, Pakistan
Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
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Abstract

In this paper, we prove some results on the Hausdorff partial b-metrics. We prove some new Lemmas regarding convergence of the sequences in the Hausdorff partial b-metric spaces. The obtained results generalize and improve many existing fixed-point results. The examples are given for the explanation of theory. The existence of the solution to the boundary value problem is proved via fixed-point approach.

Keywords

fixed pointmultivalued almost contractionspartial b-metric spaceapplication
CLC number: 47H09, 47H10, 54H25

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8188-8205
DOI: 10.3934/math.2022456

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Cite this article:
Anwar S, Nazam M, Sulami HHA, et al. Existence fixed-point theorems in the partial b-metric spaces and an application to the boundary value problem. AIMS Mathematics, 2022, 7(5): 8188-8205. https://doi.org/10.3934/math.2022456

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Received: 04 November 2021
Revised: 16 February 2022
Accepted: 17 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)