On multivalued maps for $ \varphi $-contractions involving orbits with application

Amjad Ali; Muhammad Arshad; Awais Asif; Ekrem Savas; Choonkil Park; Dong Yun Shin; Amjad Ali; Muhammad Arshad; Awais Asif; Ekrem Savas; Choonkil Park; Dong Yun Shin

doi:10.3934/math.2021440

AIMS Mathematics

2021, Volume 6, Issue 7: 7532-7554. doi: 10.3934/math.2021440

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Research article

On multivalued maps for $ \varphi $-contractions involving orbits with application

1.
Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan
2.
Department of Mathematics, Istanbul Commerce University of Turkey, Turkey
3.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
4.
Department of Mathematics, University of Seoul, Seoul 02504, Korea

Received: 12 November 2020 Accepted: 06 May 2021 Published: 08 May 2021
MSC : 47H10, 54H25

In ^[14], Proinov established the existence of fixed point theorems regarding as a generalization of the Banach contraction principle (BCP) of self mapping under an influence of gauge function (GF). In this paper, we develop some existence results on $ \varphi $-contraction for multivalued maps via $ b $-Bianchini-Grandolfi gauge function (B-GGF) in class of $ b $-metric spaces and consequently assure the existence results in the module of simulation function as well $ \alpha $-admissible mapping. An extensive set of nontrivial example is given to justify our claim. At the end, we give an application to prove the existence behavior for the system of integral inclusion.
- fixed point,
- $ b $-Bianchini-Grandolfi gauge function,
- simulation function,
- $ b $-metric space
Citation: Amjad Ali, Muhammad Arshad, Awais Asif, Ekrem Savas, Choonkil Park, Dong Yun Shin. On multivalued maps for $ \varphi $-contractions involving orbits with application[J]. AIMS Mathematics, 2021, 6(7): 7532-7554. doi: 10.3934/math.2021440

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Abstract

In ^[14], Proinov established the existence of fixed point theorems regarding as a generalization of the Banach contraction principle (BCP) of self mapping under an influence of gauge function (GF). In this paper, we develop some existence results on $ \varphi $-contraction for multivalued maps via $ b $-Bianchini-Grandolfi gauge function (B-GGF) in class of $ b $-metric spaces and consequently assure the existence results in the module of simulation function as well $ \alpha $-admissible mapping. An extensive set of nontrivial example is given to justify our claim. At the end, we give an application to prove the existence behavior for the system of integral inclusion.

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