Fixed point results for generalized contractions in controlled metric spaces with applications

Zhenhua Ma; Jamshaid Ahmad; Abdullah Eqal Al-Mazrooei; Zhenhua Ma; Jamshaid Ahmad; Abdullah Eqal Al-Mazrooei

doi:10.3934/math.2023025

AIMS Mathematics

2023, Volume 8, Issue 1: 529-549. doi: 10.3934/math.2023025

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Fixed point results for generalized contractions in controlled metric spaces with applications

1.
Department of Mathematics and Physics, Hebei University of Architecture, Zhangjiakou 075024, China
2.
Department of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
3.
Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 06 August 2022 Revised: 05 September 2022 Accepted: 14 September 2022 Published: 09 October 2022
MSC : 46S40, 47H10, 54H25

The purpose of this article is to establish some common fixed point results for generalized contractions including some precise control functions of two variables in the setting of controlled metric spaces. As consequences of our leading results, we derive common fixed point and fixed point results for contractions with control functions of one variable and constants. We also discuss controlled metric spaces endowed with a graph and obtain some common fixed point results in this newly introduced space. As an application of our leading result, we examine the solution of a Fredholm type integral equation.
- fixed point,
- controlled metric spaces,
- control function,
- graph,
- Fredholm type integral equation
Citation: Zhenhua Ma, Jamshaid Ahmad, Abdullah Eqal Al-Mazrooei. Fixed point results for generalized contractions in controlled metric spaces with applications[J]. AIMS Mathematics, 2023, 8(1): 529-549. doi: 10.3934/math.2023025

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Abstract

The purpose of this article is to establish some common fixed point results for generalized contractions including some precise control functions of two variables in the setting of controlled metric spaces. As consequences of our leading results, we derive common fixed point and fixed point results for contractions with control functions of one variable and constants. We also discuss controlled metric spaces endowed with a graph and obtain some common fixed point results in this newly introduced space. As an application of our leading result, we examine the solution of a Fredholm type integral equation.

References

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