Existence of fixed points of generalized set-valued $ F $-contractions of $ b $-metric spaces

Basit Ali; Hafiza Aqsa Butt; Manuel De la Sen; Basit Ali; Hafiza Aqsa Butt; Manuel De la Sen

doi:10.3934/math.2022990

AIMS Mathematics

2022, Volume 7, Issue 10: 17967-17988. doi: 10.3934/math.2022990

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Research article

Existence of fixed points of generalized set-valued $ F $-contractions of $ b $-metric spaces

1.
Department of Mathematics, School of Science, University of Management and Technology, C-II, Johar Town, Lahore 54770, Pakistan
2.
Department of Mathematics, The Sahara College Narowal, Narowal, Punjab, Pakistan
3.
Department of Electricity and Electronics, Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country (UPV/EHU), Campus of Leioa, 48940 Leioa, Bizkaia, Spain

Received: 28 March 2022 Revised: 14 July 2022 Accepted: 18 July 2022 Published: 05 August 2022
MSC : Primary 47H10, 47H04, 54E99, Secondary 54H25

This paper deals with the existence of non-empty fixed point sets of newly introduced generalized set-valued $ F $-contractions of $ b $-metric spaces. Some illustrative examples show that the new results in this paper generalize properly, unify and extend some related results in the existing literature. Moreover, we extract some important consequences of the results in $ b $-metric spaces. Particularly, by setting $ b $-metric constant equal to one, we obtain some specific cases showing notable enhancement of existing results yet in metric spaces.
- $ b $-metric,
- fixed points,
- set-valued mapping,
- $ F $-contractions,
- almost $ F $-contractions
Citation: Basit Ali, Hafiza Aqsa Butt, Manuel De la Sen. Existence of fixed points of generalized set-valued $ F $-contractions of $ b $-metric spaces[J]. AIMS Mathematics, 2022, 7(10): 17967-17988. doi: 10.3934/math.2022990

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Abstract

This paper deals with the existence of non-empty fixed point sets of newly introduced generalized set-valued $ F $-contractions of $ b $-metric spaces. Some illustrative examples show that the new results in this paper generalize properly, unify and extend some related results in the existing literature. Moreover, we extract some important consequences of the results in $ b $-metric spaces. Particularly, by setting $ b $-metric constant equal to one, we obtain some specific cases showing notable enhancement of existing results yet in metric spaces.

References

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