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 , 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.
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| Martin Bohner |
Missouri University of Science and Technology
Department of Mathematics and Statistics
Rolla, Missouri 65409-0020, USA
| Jaqueline G. Mesquita |
Universidade de Brasília
Departamento de Matemática
Campus Universitário Darcy Ribeiro, Asa Norte 70910-900
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