Some fixed point results based on contractions of new types for extended $ b $-metric spaces

Wasfi Shatanawi; Taqi A. M. Shatnawi; Wasfi Shatanawi; Taqi A. M. Shatnawi

doi:10.3934/math.2023554

AIMS Mathematics

2023, Volume 8, Issue 5: 10929-10946. doi: 10.3934/math.2023554

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Research article

Some fixed point results based on contractions of new types for extended $ b $-metric spaces

Wasfi Shatanawi ^{1,2
,
,},
Taqi A. M. Shatnawi ²

1.
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan

Received: 22 November 2022 Revised: 23 February 2023 Accepted: 26 February 2023 Published: 07 March 2023
MSC : 37C25, 47H10, 54H25

The construction of contraction conditions plays an important role in science for formulating new findings in fixed point theories of mappings under a set of specific conditions. The aim of this work is to take advantage of the idea of extended $ b $-metric spaces in the sense introduced by Kamran et al. [A generalization of $ b $-metric space and some fixed point theorems, Mathematics, 5 (2017), 1–7] to construct new contraction conditions to obtain new results related to fixed points. Our results enrich and extend some known results from $ b $-metric spaces to extended b-metric spaces. We construct some examples to show the usefulness of our results. Also, we provide some applications to support our results.
- fixed point,
- extended metric space of type $ (\gamma, \beta) $,
- extended $ b $-metric space
Citation: Wasfi Shatanawi, Taqi A. M. Shatnawi. Some fixed point results based on contractions of new types for extended $ b $-metric spaces[J]. AIMS Mathematics, 2023, 8(5): 10929-10946. doi: 10.3934/math.2023554

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Abstract

The construction of contraction conditions plays an important role in science for formulating new findings in fixed point theories of mappings under a set of specific conditions. The aim of this work is to take advantage of the idea of extended $ b $-metric spaces in the sense introduced by Kamran et al. [A generalization of $ b $-metric space and some fixed point theorems, Mathematics, 5 (2017), 1–7] to construct new contraction conditions to obtain new results related to fixed points. Our results enrich and extend some known results from $ b $-metric spaces to extended b-metric spaces. We construct some examples to show the usefulness of our results. Also, we provide some applications to support our results.

References

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