The q-analogue of the epsilon(2;1)-transform and its applications

Abstract

In this paper, we introduce a new integral transform (q)epsilon(2;1), which is the q-analogue of the epsilon(2;1)-transform and can be regarded as a q-extension of the epsilon(2;1)-transform. Some identities involving L-q(2)-transfom, L-q(2)-transfom, and P-q-transform are given. By making use of these identities and (q)epsilon(2;1)-transform, a new Parseval-Goldstein type theorem is obtained. Some examples are also given as an illustration of the main results presented here.