Research Article

Semi-c-periodicity, c-uniform recurrence and almost automorphy in the complex plane

Published in: Quaestiones Mathematicae
Volume 47 , issue 12 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 2399–2428
DOI: 10.2989/16073606.2024.2371838
Author(s): H. Ounis University of Alicante, Spain, J.M. Sepulcre University of Alicante, Spain,
Keywords: 42A75, 43A60, 30Axx, 30D20, Almost periodic functions, almost periodicity, c-almost periodic functions, semi-c-periodic functions, c-uniformly recurrent functions, almost automorphic functions, asymptotic c-almost periodicity,
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Abstract

This paper is devoted to develop the concepts of semi-c-periodicity, c-uniform recurrence and almost automorphy for functions defined on vertical strips in the complex plane, where c is a non-zero complex number. As an extension of the study performed for functions defined on the real axis, this work aims to investigate the main properties of these classes of functions and establish their connections with the more known class of c-almost periodic functions defined on vertical strips. In fact, we resolve an open problem which was raised in 2020 for the real case. Additionally, we also use this approach to introduce an asymptotic version of these new classes of functions.
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