Towards coupled coincidence theorems of generalized admissible types of mappings on partial satisfactory cone metric spaces and some applications

Nashat Faried; Sahar Mohamed Ali Abou Bakr; H. Abd El-Ghaffar; S. S. Solieman Almassri; Nashat Faried; Sahar Mohamed Ali Abou Bakr; H. Abd El-Ghaffar; S. S. Solieman Almassri

doi:10.3934/math.2023425

AIMS Mathematics

2023, Volume 8, Issue 4: 8431-8459. doi: 10.3934/math.2023425

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Research article

Towards coupled coincidence theorems of generalized admissible types of mappings on partial satisfactory cone metric spaces and some applications

Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11517, Egypt

Received: 29 July 2022 Revised: 25 November 2022 Accepted: 14 December 2022 Published: 03 February 2023
MSC : 47H09, 47H10

This paper introduces a novel class of generalized $ {\alpha} $-admissible contraction types of mappings in the framework of $ {\theta} $-complete partial satisfactory cone metric spaces and proves the existence and uniqueness of coincidence points for such mappings. In this setting, the topology generated and induced by the partial satisfactory cone metric is associated with semi-interior points rather than interior points of the underlying cone. In addition, some applications of the paper's main coincidence point theorems are given. The results of this paper unify, extend and generalize some previously proved theorems in this generalized setting.
- normal cones,
- solid cones,
- partial satisfactory cone metric spaces,
- semi-interior points,
- admissible mappings,
- fixed-points,
- coincidence points,
- coupled coincidence points,
- coupled fixed-points
Citation: Nashat Faried, Sahar Mohamed Ali Abou Bakr, H. Abd El-Ghaffar, S. S. Solieman Almassri. Towards coupled coincidence theorems of generalized admissible types of mappings on partial satisfactory cone metric spaces and some applications[J]. AIMS Mathematics, 2023, 8(4): 8431-8459. doi: 10.3934/math.2023425

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Abstract

This paper introduces a novel class of generalized $ {\alpha} $-admissible contraction types of mappings in the framework of $ {\theta} $-complete partial satisfactory cone metric spaces and proves the existence and uniqueness of coincidence points for such mappings. In this setting, the topology generated and induced by the partial satisfactory cone metric is associated with semi-interior points rather than interior points of the underlying cone. In addition, some applications of the paper's main coincidence point theorems are given. The results of this paper unify, extend and generalize some previously proved theorems in this generalized setting.

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