Almost Periodic Solutions of Abstract Impulsive Volterra Integro-Differential Inclusions

Abstract

In this paper, we introduce and systematically analyze the classes of (pre-)(B,ρ,(tk))-piecewise continuous almost periodic functions and (pre-)(B,ρ,(tk))-piecewise continuous uniformly recurrent functions with values in complex Banach spaces. We weaken substantially, or remove completely, the assumption that the sequence (tk) of possible first kind discontinuities of the function under consideration is a Wexler sequence (in order to achieve these aims, we use certain results about Stepanov almost periodic type functions). We provide many applications in the analysis of the existence and uniqueness of almost periodic type solutions for various classes of the abstract impulsive Volterra integro-differential inclusions.

Keywords

• (<i>ℬ</i>,<i>ρ</i>,(<i>t_k</i>))-piecewise continuous almost periodic type functions
• (<i>ℬ</i>,<i>ρ</i>,(<i>t_k</i>))-piecewise continuous uniformly recurrent type functions
• Wexler sequences
• abstract impulsive Volterra integro-differential inclusions
• almost periodic type solutions