Electron. J. Differential Equations, Vol. 2018 (2018), No. 197, pp. 1-11.

Almost periodic functions in quantum calculus

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 $\mathbb N_0$, proving several important properties for this class of functions. We investigate the existence of almost periodic solutions of linear and nonlinear $q$-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.

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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
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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