A new approach to infinite systems of integral equations in Fréchet function spaces

Abstract

This paper proposes a more effective method for investigating the solvability of infinite systems of nonlinear integral equations than the approaches based on Banach spaces, which have been employed in a series of publications over the past several years. The study begins with a discussion of certain Fréchet function spaces, a characterization of compactness within them, and the construction of optimal families of measures of noncompactness. Subsequently, this technique of Fréchet measures of noncompactness is applied to a particular infinite system of equations. The obtained results yield significantly weaker assumptions ensuring the existence of solutions compared to those required in another publication, in which the same system was analyzed using a less efficient Banach space–based method.