Notes on <i>q</i>-Gamma Operators and Their Extension to Classes of Generalized Distributions

Abstract

This paper discusses definitions and properties of q-analogues of the gamma integral operator and its extension to classes of generalized distributions. It introduces q-convolution products, symmetric q-delta sequences and q-quotients of sequences, and establishes certain convolution theorems. The convolution theorems are utilized to accomplish q-equivalence classes of generalized distributions called q-Boehmians. Consequently, the q-gamma operators are therefore extended to the generalized spaces and performed to coincide with the classical integral operator. Further, the generalized q-gamma integral is shown to be linear, sequentially continuous and continuous with respect to some involved convergence equipped with the generalized spaces.

Keywords

• <i>q</i>-derivative
• <i>q</i>-Boehmians
• generalized symmetric distribution
• <i>q</i>-hypergeometric function
• <i>p</i>-differential operators