A novel approach of multi-valued contraction results on cone metric spaces with an application

Saif Ur Rehman; Iqra Shamas; Shamoona Jabeen; Hassen Aydi; Manuel De La Sen; Saif Ur Rehman; Iqra Shamas; Shamoona Jabeen; Hassen Aydi; Manuel De La Sen

doi:10.3934/math.2023630

AIMS Mathematics

2023, Volume 8, Issue 5: 12540-12558. doi: 10.3934/math.2023630

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Research article

A novel approach of multi-valued contraction results on cone metric spaces with an application

1.
Institute of Numerical Sciences, Department of Mathematics, Gomal University, Dera Ismail Khan 29050, Pakistan
2.
Department of Mathematics, University of Science and Technology, Bannu 28100, KP, Pakistan
3.
Université de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication H. Sousse 4000, Tunisia
4.
Department of Medical Research, 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 Electricity and Electronics, Institute of Research and Development of Processes Faculty of Science and Technology, University of the Basque Country Campus of Leioa, Leioa (Bizkaia) 48940, Spain

Received: 05 December 2022 Revised: 12 March 2023 Accepted: 15 March 2023 Published: 27 March 2023
MSC : 47H07, 47H10, 54H25

In this paper, we present some generalized multi-valued contraction results on cone metric spaces. We use some maximum and sum types of contractions for a pair of multi-valued mappings to prove some common fixed point theorems on cone metric spaces without the condition of normality. We present an illustrative example for multi-valued contraction mappings to support our work. Moreover, we present a supportive application of nonlinear integral equations to validate our work. This new theory, can be modified in different directions for multi-valued mappings to prove fixed point, common fixed point and coincidence point results in the context of different types of metric spaces with the application of different types of integral equations.
- common fixed point,
- contraction conditions,
- integral equations,
- cone metric space
Citation: Saif Ur Rehman, Iqra Shamas, Shamoona Jabeen, Hassen Aydi, Manuel De La Sen. A novel approach of multi-valued contraction results on cone metric spaces with an application[J]. AIMS Mathematics, 2023, 8(5): 12540-12558. doi: 10.3934/math.2023630

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Abstract

In this paper, we present some generalized multi-valued contraction results on cone metric spaces. We use some maximum and sum types of contractions for a pair of multi-valued mappings to prove some common fixed point theorems on cone metric spaces without the condition of normality. We present an illustrative example for multi-valued contraction mappings to support our work. Moreover, we present a supportive application of nonlinear integral equations to validate our work. This new theory, can be modified in different directions for multi-valued mappings to prove fixed point, common fixed point and coincidence point results in the context of different types of metric spaces with the application of different types of integral equations.

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