Hybrid pair of multivalued mappings in modular-like metric spaces and applications

Tahair Rasham; Muhammad Nazam; Hassen Aydi; Abdullah Shoaib; Choonkil Park; Jung Rye Lee; Tahair Rasham; Muhammad Nazam; Hassen Aydi; Abdullah Shoaib; Choonkil Park; Jung Rye Lee

doi:10.3934/math.2022590

AIMS Mathematics

2022, Volume 7, Issue 6: 10582-10595. doi: 10.3934/math.2022590

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Research article

Hybrid pair of multivalued mappings in modular-like metric spaces and applications

1.
Department of Mathematics, University of Poonch Rawalakot, Azad Kashmir, Pakistan
2.
Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad, Pakistan
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
6.
Department of Mathematics and Statistics, Riphah International University, Islamabad 44000, Pakistan
7.
Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Korea
8.
Department of Data Science, Daejin University, Kyunggi 11159, Korea

Received: 17 January 2022 Revised: 21 March 2022 Accepted: 24 March 2022 Published: 29 March 2022
MSC : 46Txx, 47H04, 47H10, 54H25

Our aim is to prove some new fixed point theorems for a hybrid pair of multivalued $ \alpha _{\ast } $-dominated mappings involving a generalized $ Q $-contraction in a complete modular-like metric space. Further results involving graphic contractions for a pair of multi-graph dominated mappings have been considered. Applying our obtained results, we resolve a system of nonlinear integral equations.
- fixed point,
- generalized $ Q $-contraction,
- $ \alpha _{\ast } $-dominated multivalued mapping,
- graphic contraction,
- integral equation
Citation: Tahair Rasham, Muhammad Nazam, Hassen Aydi, Abdullah Shoaib, Choonkil Park, Jung Rye Lee. Hybrid pair of multivalued mappings in modular-like metric spaces and applications[J]. AIMS Mathematics, 2022, 7(6): 10582-10595. doi: 10.3934/math.2022590

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Abstract

Our aim is to prove some new fixed point theorems for a hybrid pair of multivalued $ \alpha _{\ast } $-dominated mappings involving a generalized $ Q $-contraction in a complete modular-like metric space. Further results involving graphic contractions for a pair of multi-graph dominated mappings have been considered. Applying our obtained results, we resolve a system of nonlinear integral equations.

References

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