Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces

Direct and inverse approximation theorems are proved in the Besicovitch-Stepanets spaces $B{\mathcal S}^{p}$ of almost periodic functions in terms of the best approximations of functions and their generalized moduli of smoothness.

N-dimensional almost periodic functions II

In this paper we continue the research begun in [CA-2]. Some new results are shown and proven, like the structure theorem for n-dimensional almost periodic functions by using the Bochner Transform. Also, the Haraux [Har] condition in the n-dimensional case, and some topological theorems similar to Bochner and Ascoli theorems. Furthermore, we answer a question formulated by Prof. Fischer [Fis], and we study an average theorem for integrals of almost periodic functions.

(&omega,c)- PSEUDO ALMOST PERIODIC FUNCTIONS, (&omega,c)- PSEUDO ALMOST AUTOMORPHIC FUNCTIONS AND APPLICATIONS

In this paper, we introduce the classes of $(\omega, c)$-pseudo almost periodicfunctions and $(\omega, c)$-pseudo almost automorphicfunctions. These collections include $(\omega, c)$-pseudo periodicfunctions, pseudo almost periodic functions and their automorphic analogues.We present an application to the abstract semilinear first-order Cauchy inclusions in Banach spaces.

Almost Periodic Functions and Their Applications: A Survey of Results and Perspectives

The main aim of this survey article is to present several known results about vector-valued almost periodic functions and their applications. We separately consider almost periodic functions depending on one real variable and almost periodic functions depending on two or more real variables. We address several open problems and possibilities for further investigations of almost periodic functions, quoting more than two hundred references about the subject under our consideration.