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

Semi-Bloch periodic functions, semi-anti-periodic functions and applications