Extension of generalized Fox’s H-function operator to certain set of generalized integrable functions

Abstract

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.

Keywords

• H̄-function
• H-function
• Hypergeomatric functions
• Mittag-Leffler functions
• Boehmians