Pseudo asymptotically periodic mild solutions of semilinear functional integro-differential equations in Banach spaces.

In this paper, we introduce and investigate the functions of ( μ, ν)-pseudo S-asymptotically ω-periodic of class r(class infinity). We systematically explore the properties of these functions in Banach space including composition theorems. As applications, we establish some sufficient criteria for ( μ, ν)-pseudo S-asymptotic ω-periodicity of (nonautonomous) semilinear integro-differential equations with finite or infinite delay. Finally, some interesting examples are presented to illustrate the main findings. [ABSTRACT FROM AUTHOR]