A β-Convolution Theorem Associated with the General Quantum Difference Operator. (24th February 2022)

• Record Type: Journal Article
• Authors: Shehata, Enas M.; El Zafarani, Rasha M.
• Other Names: Youssri Youssri Hassan Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-02-24
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/1581362
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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, D β f t = f β t − f t / β t − 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.