28, May 2025

Generalization of Mellin-Stieltjes Transform and its Analytical Structure

VOLUME-11; ISSUE-5; MAY-2025

Author(s): 1. A. N. Rangari, 2. R. S. Tathod, 3. V. D. Sharma

Authors Affiliations:

1 Department of Mathematics, Adarsh College, Dhamangaon Rly.- 444709 (M.S), India.

2 Department of Mathematics, Shri Shivaji Science College, Amravati, (M.S.), India.

3Department of Mathematics, Arts, Commerce and Science College, Amravati- 444606(M.S), India.

DOIs:10.2015/IJIRMF/202505018     |     Paper ID: IJIRMF202505018


Abstract
Keywords
References
Integral Transform is a mathematical operator that transform a function from one space to another space via integration. It is a powerful mathematical tool with a range of applications across various fields.  It transforms very complicated differential equation into simpler ones. There are so many integral transforms and each have special contribution in application field. We have reviewed various types of integral transform which are available in the literature and see that Mellin and Stieltjes transform have special efforts to solving difficult problems in science and engineering. So, we have tried to form a new integral transform that is Mellin-Stieltjes transform in the distributional sense. Present paper gives the generalization of Mellin-Stieltjes Transform in the distributional sense. We first define definition of generalized Mellin-Stieltjes Transform, also define some testing function space. The main purpose of this paper is to prove the Analyticity theorem by keeping some parameters fixed.
Mellin Transform, Stieltjes Transform, Mellin-Stieltjes Transform, Generalized function, Testing function space.
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