In this paper, we introduce a new class of functions, called strongly Stepanov–Orlicz pseudo-almost periodic functions, which extends Zhang’s pseudo-almost periodicity to the Stepanov–Orlicz framework. These functions are defined as the sum of two components taking values in a common space \(\mathbb {X}\) , which is endowed with both a Banach and a modular structure: a Stepanov–Orlicz almost periodic function, defined as the norm-limit of generalized trigonometric polynomials, and a strongly modular ergodic function, studied within the modular framework of \(\mathbb {X}\) . Several structural properties of this new class are established, including completeness, stability under addition and scalar multiplication, translation invariance, as well as a convolution result under suitable integrability conditions. We also construct a concrete example illustrating this new class of functions. In addition, we examine the existence and uniqueness of mild solutions to evolution equations within this framework, and provide an illustrative application.
