New fixed point results in controlled metric type spaces based on new contractive conditions

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

doi:10.3934/math.2023468

AIMS Mathematics

2023, Volume 8, Issue 4: 9314-9330. doi: 10.3934/math.2023468

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Research article

New fixed point results in controlled metric type spaces based on new contractive conditions

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: 06 December 2022 Revised: 23 January 2023 Accepted: 01 February 2023 Published: 15 February 2023
MSC : 37C25, 47H10, 54H25

In the present work, we will establish and prove some fixed point theorems for mappings that satisfy a set of conditions in controlled metric type spaces introduced by Mlaiki et al. [N. Mlaiki, H. Aydi, N. Souayah, T. Abdeljawad, Controlled metric type spaces and the related contraction principle. Mathematics 2018, 6,194]. Our technique in constructing our new contraction conditions is to insert the control function $ \theta(u, l) $ that appears on the right hand side of the triangular inequality of the definition of the controlled metric spaces in the right hand side of our proposed contraction conditions. Our results enrich the field of fixed point theory with novel findings that generalize many findings found in the literature. We provide an example to show the usefulness of our results. Also, we present an application to our results to show their significance.
- fixed point,
- controlled metric space of type $ (\gamma, \beta) $,
- extended b-metric space
Citation: Wasfi Shatanawi, Taqi A. M. Shatnawi. New fixed point results in controlled metric type spaces based on new contractive conditions[J]. AIMS Mathematics, 2023, 8(4): 9314-9330. doi: 10.3934/math.2023468

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Abstract

In the present work, we will establish and prove some fixed point theorems for mappings that satisfy a set of conditions in controlled metric type spaces introduced by Mlaiki et al. [N. Mlaiki, H. Aydi, N. Souayah, T. Abdeljawad, Controlled metric type spaces and the related contraction principle. Mathematics 2018, 6,194]. Our technique in constructing our new contraction conditions is to insert the control function $ \theta(u, l) $ that appears on the right hand side of the triangular inequality of the definition of the controlled metric spaces in the right hand side of our proposed contraction conditions. Our results enrich the field of fixed point theory with novel findings that generalize many findings found in the literature. We provide an example to show the usefulness of our results. Also, we present an application to our results to show their significance.

References

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