Periodic and fixed points for $ F $-type contractions in $ b $-gauge spaces

Nosheen Zikria; Aiman Mukheimer; Maria Samreen; Tayyab Kamran; Hassen Aydi; Kamal Abodayeh; Nosheen Zikria; Aiman Mukheimer; Maria Samreen; Tayyab Kamran; Hassen Aydi; Kamal Abodayeh

doi:10.3934/math.20221013

AIMS Mathematics

2022, Volume 7, Issue 10: 18393-18415. doi: 10.3934/math.20221013

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Periodic and fixed points for $ F $-type contractions in $ b $-gauge spaces

1.
Department of Mathematics, Quaid-i-Azam university, Islamabad, Pakistan
2.
Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
3.
Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, Tunisia
4.
China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
5.
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

Received: 29 May 2022 Revised: 09 August 2022 Accepted: 12 August 2022 Published: 17 August 2022
MSC : 47H10, 54H25

In this paper, we introduce $ \mathcal{J}_{s; \Omega} $-families of generalized pseudo-$ b $-distances in $ b $-gauge spaces $ (U, {Q}_{s; \Omega}) $. Moreover, by using these $ \mathcal{J}_{s; \Omega} $-families on $ U $, we define the $ \mathcal{J}_{s; \Omega} $-sequential completeness and construct an $ F $-type contraction $ T:U\rightarrow U $. Furthermore, we develop novel periodic and fixed point results for these mappings in the setting of $ b $-gauge spaces using $ \mathcal{J}_{s; \Omega} $-families on $ U $, which generalize and improve some of the results in the corresponding literature. The validity and importance of our theorems are shown through an application via an existence solution of an integral equation.
- $ b $-gauge space,
- generalized pseudo-$ b $-distance,
- $ F $-contraction,
- fixed point,
- periodic point
Citation: Nosheen Zikria, Aiman Mukheimer, Maria Samreen, Tayyab Kamran, Hassen Aydi, Kamal Abodayeh. Periodic and fixed points for $ F $-type contractions in $ b $-gauge spaces[J]. AIMS Mathematics, 2022, 7(10): 18393-18415. doi: 10.3934/math.20221013

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Abstract

In this paper, we introduce $ \mathcal{J}_{s; \Omega} $-families of generalized pseudo-$ b $-distances in $ b $-gauge spaces $ (U, {Q}_{s; \Omega}) $. Moreover, by using these $ \mathcal{J}_{s; \Omega} $-families on $ U $, we define the $ \mathcal{J}_{s; \Omega} $-sequential completeness and construct an $ F $-type contraction $ T:U\rightarrow U $. Furthermore, we develop novel periodic and fixed point results for these mappings in the setting of $ b $-gauge spaces using $ \mathcal{J}_{s; \Omega} $-families on $ U $, which generalize and improve some of the results in the corresponding literature. The validity and importance of our theorems are shown through an application via an existence solution of an integral equation.

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