Some Estimates for Certain <i>q</i>-analogs of Gamma Integral Transform Operators

Abstract

The aim of this work is to examine some q-analogs and differential properties of the gamma integral operator and its convolution products. The q-gamma integral operator is introduced in two versions in order to derive pertinent conclusions regarding the q-exponential functions. Also, new findings on the q-trigonometric, q-sine, and q-cosine functions are extracted. In addition, novel results for first and second-order q-differential operators are established and extended to Heaviside unit step functions. Lastly, three crucial convolution products and extensive convolution theorems for the q-analogs are also provided.

Keywords

• <i>q</i>-gamma operator
• integral operator
• <i>q</i>-analogs
• differential operator
• symmetrical polynomials