Extension of generalized Fox’s H-function operator to certain set of generalized integrable functions
Abstract In this article, we investigate the so-called Inayat integral operator T p , q m , n $T_{p,q}^{m,n}$ , p , q , m , n ∈ Z $p,q,m,n\in \mathbb{Z}$ , 1 ≤ m ≤ q $1\leq m\leq q$ , 0 ≤ n ≤ p $0\leq n\leq p $ , on classes of generalized integrable functions. We make use of the Mellin-type convolut...
Main Author: | |
---|---|
Format: | Article |
Language: | English |
Published: |
SpringerOpen
2020-08-01
|
Series: | Advances in Difference Equations |
Subjects: | |
Online Access: | http://link.springer.com/article/10.1186/s13662-020-02910-8 |
id |
doaj-ef6c03807c134b778c6e2161025f761b |
---|---|
record_format |
Article |
spelling |
doaj-ef6c03807c134b778c6e2161025f761b2020-11-25T03:55:13ZengSpringerOpenAdvances in Difference Equations1687-18472020-08-012020111110.1186/s13662-020-02910-8Extension of generalized Fox’s H-function operator to certain set of generalized integrable functionsShrideh Khalaf Al-Omari0Department of Physics and Applied Sciences, Faculty of Engineering Technology, Al-Balqa Applied UniversityAbstract In this article, we investigate the so-called Inayat integral operator T p , q m , n $T_{p,q}^{m,n}$ , p , q , m , n ∈ Z $p,q,m,n\in \mathbb{Z}$ , 1 ≤ m ≤ q $1\leq m\leq q$ , 0 ≤ n ≤ p $0\leq n\leq p $ , on classes of generalized integrable functions. We make use of the Mellin-type convolution product and produce a concurrent convolution product, which, taken together, establishes the Inayat integral convolution theorem. The Inayat convolution theorem and a class of delta sequences were derived and employed for constructing sequence spaces of Boehmians. Moreover, by the aid of the concept of quotients of sequences, we present a generalization of the Inayat integral operator in the context of Boehmians. Various results related to the generalized integral operator and its inversion formula are also derived.http://link.springer.com/article/10.1186/s13662-020-02910-8H̄-functionH-functionHypergeomatric functionsMittag-Leffler functionsBoehmians |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Shrideh Khalaf Al-Omari |
spellingShingle |
Shrideh Khalaf Al-Omari Extension of generalized Fox’s H-function operator to certain set of generalized integrable functions Advances in Difference Equations H̄-function H-function Hypergeomatric functions Mittag-Leffler functions Boehmians |
author_facet |
Shrideh Khalaf Al-Omari |
author_sort |
Shrideh Khalaf Al-Omari |
title |
Extension of generalized Fox’s H-function operator to certain set of generalized integrable functions |
title_short |
Extension of generalized Fox’s H-function operator to certain set of generalized integrable functions |
title_full |
Extension of generalized Fox’s H-function operator to certain set of generalized integrable functions |
title_fullStr |
Extension of generalized Fox’s H-function operator to certain set of generalized integrable functions |
title_full_unstemmed |
Extension of generalized Fox’s H-function operator to certain set of generalized integrable functions |
title_sort |
extension of generalized fox’s h-function operator to certain set of generalized integrable functions |
publisher |
SpringerOpen |
series |
Advances in Difference Equations |
issn |
1687-1847 |
publishDate |
2020-08-01 |
description |
Abstract In this article, we investigate the so-called Inayat integral operator T p , q m , n $T_{p,q}^{m,n}$ , p , q , m , n ∈ Z $p,q,m,n\in \mathbb{Z}$ , 1 ≤ m ≤ q $1\leq m\leq q$ , 0 ≤ n ≤ p $0\leq n\leq p $ , on classes of generalized integrable functions. We make use of the Mellin-type convolution product and produce a concurrent convolution product, which, taken together, establishes the Inayat integral convolution theorem. The Inayat convolution theorem and a class of delta sequences were derived and employed for constructing sequence spaces of Boehmians. Moreover, by the aid of the concept of quotients of sequences, we present a generalization of the Inayat integral operator in the context of Boehmians. Various results related to the generalized integral operator and its inversion formula are also derived. |
topic |
H̄-function H-function Hypergeomatric functions Mittag-Leffler functions Boehmians |
url |
http://link.springer.com/article/10.1186/s13662-020-02910-8 |
work_keys_str_mv |
AT shridehkhalafalomari extensionofgeneralizedfoxshfunctionoperatortocertainsetofgeneralizedintegrablefunctions |
_version_ |
1724469979120664576 |