Meir-Keeler Condensing Operators and a Family of Measures of Noncompactness in Frechet Spaces

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 Frchet space, and present a generalization of the Darbo theorem.Additionally, we state the notion of an -variable MK condensing operator regarding an FMN and extend our findings to the -variable context.To support our main results, we demonstrate the existence of solutions for a class of systems of -variable functional Volterra integral equations, which can generalize many standard and couple systems.