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

Abstract

AbstractIn this article, we investigate the so-called Inayat integral operator $T_{p,q}^{m,n}$ T p , q m , n , $p,q,m,n\in \mathbb{Z}$ p , q , m , n ∈ Z , $1\leq m\leq q$ 1 ≤ m ≤ q , $0\leq n\leq p $ 0 ≤ n ≤ 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.