Meir-Keeler condensing operators and a family of measures of noncompactness in Fréchet spaces

F. Soltanpour^a, H. Majani^a, A. Shole Haghighi<sup>b

a</sup> Department of Mathematics Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
^b Department of Mathematics, Karaj Branch, Islamic Azad University Karaj, Iran

Abstract: In this paper, we propose the concept of Meir-Keeler (MK) condensing operators with respect to a family of measures of noncompactness (FMN) in a Fréchet space, and present a generalization of the Darbo theorem. Additionally, we state the notion of an $n$-variable MK condensing operator regarding an FMN and extend our findings to the $n$-variable context. To support our main results, we demonstrate the existence of solutions for a class of systems of $n$-variable functional Volterra integral equations, which can generalize many standard and couple systems.

Keywords: Meir-Keeler condensing operator, family of measures of noncompactness, Fréchet space, system of functional integral equations.

UDC: 517.98

MSC: 47H10, 47H08, 39B72

Received: 01.05.2025
Revised: 09.09.2025
Accepted: 16.10.2025

Language: English

DOI: 10.15393/j3.art.2025.18170