Weighted Sp-pseudo S-asymptotic periodicity and applications to Volterra integral equations

摘要

This paper is related to the function space formed by weighted Sp-pseudo S-asymptotic periodicity and their applications. Initially, the translation invariance and completeness of the function space are investigated. Additionally, the composition theorem and convolution operator generated by Lebesgue integrable functions are presented. Finally, existence and uniqueness of solutions with weighted Sp-pseudo S-asymptotic periodicity for two classes of Volterra equations are proved by using the results obtained above, and some concrete examples are given. The methods mainly include Minkowski’s inequality, convolution inequality, contraction mapping principle, and especially the generalized Minkowski’s inequality. Our results extend some known results on asymptotic periodicity.