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Research Article | Open Access

Double controlled M-metric spaces and some fixed point results

Fahim Uddin1, Faizan Adeel2, Khalil Javed2, Choonkil Park3( ), Muhammad Arshad2
Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan
Department of Mathematics and Statistic, International Islamic University, Islamabad, Pakistan
Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Korea
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Abstract

In this article, we introduce the idea of double controlled M-metric space by employing two control functions a ( u , w ) and β ( w , v ) on the right-hand side of the triangle inequality of M-metric space. We provide some examples of double controlled M-metric spaces. We also provide some fixed point results under new type of contractions in the setting of double controlled M-metric spaces. Moreover, we give an example to highlight the importance of one of our main results.

Keywords

fixed pointFredholm integral equationdouble controlled M-metric space
CLC number: 47H10, 54H25

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AIMS Mathematics
Volume 7 Issue 8,
August 2022
Pages 15298-15312
DOI: 10.3934/math.2022838

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Cite this article:
Uddin F, Adeel F, Javed K, et al. Double controlled M-metric spaces and some fixed point results. AIMS Mathematics, 2022, 7(8): 15298-15312. https://doi.org/10.3934/math.2022838

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Received: 02 April 2022
Revised: 07 June 2022
Accepted: 13 June 2022
Published: 15 August 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)