Equicontinuity, affine mean ergodic theorem and linear equations in random normed spaces

Abstract

The aim of this paper is to give a characterization of equicontinuous families of linear operators in random normed spaces which generalizes the normed spaces case. This characterization is used to generalize some results on iterative solutions of linear equations by using the affine mean ergodic theorem for locally convex spaces (note that every Fr 'echet space is a random normed space with the t t -norm T = Min T = {\text {Min}} ).