Title: Solving coupled system of nonlinear integral and functional equation via coupled fixed point technique in G-metric space

Authors: R. Anna Thirumalai; S. Thalapathiraj

Addresses: Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Vadapalani Campus, No. 1 Jawaharlal Nehru Salai, Vadapalani, Chennai – 600026, Tamil Nadu, India ' Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Vadapalani Campus, No. 1 Jawaharlal Nehru Salai, Vadapalani, Chennai – 600026, Tamil Nadu, India

Abstract: The aim of this paper is to obtain coupled fixed point (CFP) results for an F-contraction mapping (F-CM) that fulfils a nonlinear contraction condition (CC) in the complete G-metric space (G-MS) framework, both with and without a directed graph (DG). By utilising our derived results, we discuss illustrative examples to support and illustrate some of the obtained results. Finally, we investigate the problem of existence and uniqueness of solutions for a class of functional equation systems that arise in dynamic programming and nonlinear integral equations (N LIE).

Keywords: coupled common fixed point; F-contraction mapping; G-Cauchy sequence; G-metric space; nonlinear integral equations; N LIE; dynamic programming.

DOI: 10.1504/IJMOR.2026.153617

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.1, pp.24 - 53

Received: 27 May 2024
Accepted: 11 Jun 2024
Published online: 18 May 2026 *

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