Doss ? -Almost Periodic Type Functions in R n

Marko Kostić, Wei-Shih Du and Vladimir E. Fedorov
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Marko Kostić: Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
Wei-Shih Du: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Vladimir E. Fedorov: Mathematical Analysis Department, Chelyabinsk State University, Kashirin Brothers St. 129, 454001 Chelyabinsk, Russia

Mathematics, 2021, vol. 9, issue 21, 1-27

Abstract: In this paper, we investigate various classes of multi-dimensional Doss ? -almost periodic type functions of the form F : ? × X ? Y , where n ? N , ? ? ? ? R n , X and Y are complex Banach spaces, and ? is a binary relation on Y . We work in the general setting of Lebesgue spaces with variable exponents. The main structural properties of multi-dimensional Doss ? -almost periodic type functions, like the translation invariance, the convolution invariance and the invariance under the actions of convolution products, are clarified. We examine connections of Doss ? -almost periodic type functions with ( ? , c ) -periodic functions and Weyl- ? -almost periodic type functions in the multi-dimensional setting. Certain applications of our results to the abstract Volterra integro-differential equations and the partial differential equations are given.

Keywords: Doss ? -almost periodic type functions in ? n; Lebesgue spaces with variable exponents; abstract Volterra integro-differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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