Cone $\mathfrak{C}$-class functions using $(CLR_{\Gamma \mathfrak{L} })$-property on cone $b$-normed spaces with application

K. Maheshwaran; Arslan Hojat Ansari; Stojan N Radenovic; M.S. Khan; Yumnam Mahendra Singh

doi:10.11568/kjm.2024.32.3.561

Korean J. Math. Vol. 32 No. 3 (2024) pp.561-591
DOI: https://doi.org/10.11568/kjm.2024.32.3.561

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Published: Sep 30, 2024

Keywords:

cone b-metric space,, Banach space, common fixed point, CLR-property,, normed space

Mathematics Subject Classification:

47H10, 54H25

K. Maheshwaran

Department of mathematics, School of Engineering and Technology, Dhanalakshmi Srinivasan University, Perambalur-621212,Tamil Nadu, India.

Arslan Hojat Ansari

Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa-0204, South Africa.

Stojan N Radenovic

Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade 11120, Serbia.

M.S. Khan

Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa-0204, South Africa.

Yumnam Mahendra Singh

Department of Basic Science and Humanities, Manipur Institute of Technology (A Constituent College of Manipur University), Takyelpat - 795004, India.

Abstract

In this article, we demonstrate the conditions for the existence of common fixed points $(C F P)$ theorems for four self-maps satisfying the common limit range $(C L R)$ -property on cone $b$ -normed spaces $(C b N S)$ via $C$ -class functions. Furthermore, we have a unique common fixed point for two weakly compatible $(W C)$ pairings. Towards the end, the existence and uniqueness of common solutions for systems of functional equations arising in dynamic programming are discussed as an application of our main result.

This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

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