Infinite-Class Mean Pseudo-Almost Automorphic Solutions

Abstract

This paper introduces and studies the concept of mean (η₁;η₂)-pseudo-almost automorphic solution of infinite class for stochastic processes using the measure theory. We present many interesting results on spaces, such as completeness and composition theorems. Our abstract results are then applied to the study of the existence and uniqueness of mean almost-pseudo automorphic solutions for the stochastic evolution equation. These results provide an effective framework for analyzing the existence and uniqueness of mean (η₁;η₂)-pseudo-almost automorphic solutions of infinite class of stochastic evolution equations, combining semigroup theory, fixed-point argument.