Abstract
In this paper we investigate certain integral operator involving Jacobi-Dunkl functions in a class of generalized functions. We utilize convolution products, approximating identities, and several axioms to allocate the desired spaces of generalized functions. The existing theory of the Jacobi-Dunkl integral operator (Ben Salem and Ahmed Salem in Ramanujan J. 12(3):359-378, 2006) is extended and applied to a new addressed set of Boehmians. Various embeddings and characteristics of the extended Jacobi-Dunkl operator are discussed. An inversion formula and certain convergence with respect to delta and Delta convergences are also introduced.