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

Salem A., UÇAR F.

TURKISH JOURNAL OF MATHEMATICS, vol.40, no.1, pp.98-107, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.3906/mat-1411-70
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.98-107
  • Keywords: q-Exponential integral, L-q(2)-transfom, L-q(2)-transfom, P-q-transform, q-analogue of epsilon(2;1)-transform
  • Marmara University Affiliated: Yes

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.