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

Almost periodic functions in quantum calculus

Martin Bohner, Jaqueline G. Mesquita

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.

Show me the PDF file (228 KB), TEX file for this article.

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

Return to the EJDE web page