New fixed point results in double controlled metric type spaces with applications

Fatima M. Azmi; Fatima M. Azmi

doi:10.3934/math.2023080

AIMS Mathematics

2023, Volume 8, Issue 1: 1592-1609. doi: 10.3934/math.2023080

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Research article

New fixed point results in double controlled metric type spaces with applications

Fatima M. Azmi ^,

Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia

Received: 31 August 2022 Revised: 01 October 2022 Accepted: 10 October 2022 Published: 24 October 2022
MSC : 47H10, 45B05, 54H25

The concept of an $ { \mathcal F} $-contraction was introduced by Wardowski, while Samet et al. introduced the class of $ \alpha $-admissible mappings and the concept of ($ \alpha $-$ \psi $)-contractive mapping on complete metric spaces. In this paper, we study and extend two types of contraction mappings: ($ \alpha $-$ \psi $)-contraction mapping and ($ \alpha $-$ { \mathcal F} $)-contraction mapping, and establish new fixed point results on double controlled metric type spaces. Moreover, we demonstrate some examples and present an application of our result on the existence and uniqueness of the solution for an integral equation.
- fixed point,
- double controlled metric type spaces,
- ($ \alpha-\psi $)-contraction,
- $ (\alpha $-$ { \mathcal F} $)-contraction,
- $ b $-metric spaces,
- Wardowski contractions
Citation: Fatima M. Azmi. New fixed point results in double controlled metric type spaces with applications[J]. AIMS Mathematics, 2023, 8(1): 1592-1609. doi: 10.3934/math.2023080

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Abstract

The concept of an $ { \mathcal F} $-contraction was introduced by Wardowski, while Samet et al. introduced the class of $ \alpha $-admissible mappings and the concept of ($ \alpha $-$ \psi $)-contractive mapping on complete metric spaces. In this paper, we study and extend two types of contraction mappings: ($ \alpha $-$ \psi $)-contraction mapping and ($ \alpha $-$ { \mathcal F} $)-contraction mapping, and establish new fixed point results on double controlled metric type spaces. Moreover, we demonstrate some examples and present an application of our result on the existence and uniqueness of the solution for an integral equation.

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