ALMOST PERIODIC TYPE FUNCTIONS AND DENSITIES

Marko Kostić (1)

1 Faculty of Sciences [Novi Sad]

In this paper, we introduce and analyze the notions of g-almost periodicity and Stepanov g-almost periodicity for functions with values in complex Banach spaces. In order to do that, we use the recently introduced notions of lower and upper (Banach) g-densities. We also analyze uniformly recurrent functions, generalized almost automorphic functions and apply our results in the qualitative analysis of solutions of inhomogeneous abstract integro-differential inclusions. We present plenty of illustrative examples, results of independent interest, questions and unsolved problems.

Domaines: Mathématiques [math]; Analyse fonctionnelle [math.FA]

Marko Kostić. ALMOST PERIODIC TYPE FUNCTIONS AND DENSITIES. 2020. ⟨hal-02523952⟩