New Development Theory on Measure Pseudo – Asymptotically Omega Periodic Functions

Abstract The main goal of the paper concerns two parts, in the ˝rst one, we extend some results from Blot et al [5] under general hypothesis on the measure, in the second part, we introduce a new class of functions, which we call measure pseudo 𝒮 - asymptotically omega periodic functions. The obtained results is the extension of those established recently in the literature. Then we establish many interesting results on those functions, namely their characterization, we give also several properties of those class of functions as composition results, the invariance by translation, and the convolution product. All sections are illustrated by examples or counter examples.