A β-Convolution Theorem Associated with the General Quantum Difference Operator - Enas M. Shehata; Rasha M. El Zafarani (Journal of Function Spaces)
In this paper, we prove some properties of the β-partial derivative. We define the β-convolution of two functions associated with the general quantum difference operator, Dβft=fβt−ft/βt−t; β is a strictly increasing continuous function. Moreover, we study the shift, the associative law, and the β-differentiability of the β-convolution. Furthermore, we prove the β-convolution theorem and give some applications.