  In this paper, we introduce the notions of semi-Bloch periodic functions and
semi-anti-periodic functions. Stepanov semi-Bloch periodic functions and
Stepanov semi-anti-periodic functions are considered, as well. We analyze the
invariance of introduced classes under the actions of convolution products and
briefly explain how one can use the obtained results in the qualitative
analysis of solutions of abstract inhomogeneous integro-differential equations.
