Almost periodic functions in quantum calculus

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.

Keywords

• Quantum calculus
• Jackson derivative
• periodicity
• Bochner almost periodicity
• Bohr almost periodicity