Martin Bohner, Jaqueline G. Mesquita
Abstract:
In this article, we introduce the concepts of Bochner and Bohr almost
periodic functions in quantum calculus and show that both concepts are
equivalent. Also, we present a correspondence between almost periodic
functions defined in quantum calculus and
, proving several
important properties for this class of functions. We investigate the
existence of almost periodic solutions of linear and nonlinear
-difference equations. Finally, we provide some examples of almost
periodic functions in quantum calculus.
Submitted February 1, 2018. Published December 12, 2018.
Math Subject Classifications: 39A20, 34N05, 34C25, 39A23.
Key Words: Quantum calculus; Jackson derivative; periodicity;
Bochner almost periodicity; Bohr almost periodicity.
Show me the PDF file (228 KB), TEX file for this article.
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Martin Bohner Missouri University of Science and Technology Department of Mathematics and Statistics Rolla, Missouri 65409-0020, USA email: bohner@mst.edu |
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Jaqueline G. Mesquita Universidade de Brasília Departamento de Matemática Campus Universitário Darcy Ribeiro, Asa Norte 70910-900 Brasília-DF, Brazil email: jgmesquita@unb.br |
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