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.

Integration in some new concept of ergodic functions and application to some epidemiological models

“…To state these results, the authors construct a new fixed point theorem in a cone. Similarly, for Equation (20), Xu and Yuan 28 state existence of positive almost periodic, asymptotically almost periodic, weakly almost periodic and pseudo almost periodic solutions.…”

“…Some basic facts on this type of functions were developed in Ait Dads and Lhachimi. 20 2.2 Properties of measure pseudo asymptotically omega periodic functions Proposition 2.2 (Ait Dads and Lhachimi, 20 Proposition 3.1). Let 𝜇 ∈  and 𝜔 > 0, then:…”

“…This work is organized as follows: Section 2 is divided into two subsections, the first one is devoted to notations and definitions on pseudo -asymptotically omega periodic function, and in the second one, we recall some results on pseudo -asymptotically omega periodic type functions, which are developed in the paper. 20 In Section 3, we give necessary and sufficient conditions under which the primitive of such functions remain also measure pseudo -asymptotically omega periodic. We recall some preliminaries about the Hilbert's projective metric, which will be used to prove our main results in the application.…”