Infinity Approximation of Almost Periodic Functions: Stepanov's Approach and Its Utility in Semilinear Delayed Equations on Time Scales

Abstract

ABSTRACT This article introduces, for the first time, a novel class of functions that approximate Stepanov almost periodic functions near infinity on time scales . This class includes several previously studied classes in the literature.We then explore a range of important properties of the function space associated with these functions, including completeness and composition theorems, which are crucial for addressing the solvability of certain inhomogeneous linear Cauchy problems and semilinear Cauchy problems with variable delays on . Two illustrative examples will be provided to clarify the practical application of our findings.

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