Fixed point results of a generalized reversed $ F $-contraction mapping and its application

Shahid Bashir; Naeem Saleem; Syed Muhammad Husnine; Shahid Bashir; Naeem Saleem; Syed Muhammad Husnine

doi:10.3934/math.2021507

AIMS Mathematics

2021, Volume 6, Issue 8: 8728-8741. doi: 10.3934/math.2021507

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Research article

Fixed point results of a generalized reversed $ F $-contraction mapping and its application

1.
National University of Computer and Emerging Sciences, Lahore Campus, 54700, Pakistan
2.
Department of Mathematics, University of Management and Technology, Lahore, Pakistan

Received: 19 January 2021 Accepted: 03 June 2021 Published: 08 June 2021
MSC : 47H10, 47H19, 54H25

In this paper, we introduce the reversal of generalized Banach contraction principle and mean Lipschitzian mapping respectively. Secondly, we prove the existence and uniqueness of fixed points for these expanding type mappings. Further, we extend Wardowski's idea of $ F $-contraction by introducing the reversed generalized $ F $-contraction mapping and use our obtained result to prove the existence and uniqueness of its fixed point. Finally, we apply our results to prove the existence of a unique solution of a non-linear integral equation.
- mean lipschitzian mapping,
- generalized reversed contraction mapping,
- reversed mean lipschitzian mapping,
- fixed point
Citation: Shahid Bashir, Naeem Saleem, Syed Muhammad Husnine. Fixed point results of a generalized reversed $ F $-contraction mapping and its application[J]. AIMS Mathematics, 2021, 6(8): 8728-8741. doi: 10.3934/math.2021507

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Abstract

In this paper, we introduce the reversal of generalized Banach contraction principle and mean Lipschitzian mapping respectively. Secondly, we prove the existence and uniqueness of fixed points for these expanding type mappings. Further, we extend Wardowski's idea of $ F $-contraction by introducing the reversed generalized $ F $-contraction mapping and use our obtained result to prove the existence and uniqueness of its fixed point. Finally, we apply our results to prove the existence of a unique solution of a non-linear integral equation.

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