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This paper deals with the generalized q -theory of the q -Mellin transform and its certain properties in a set of q -generalized functions. Some related q -equivalence relations, q -quotients of sequences, q -convergence definitions, and q -delta sequences are represented. Along with that, a new q -convolution theorem of the estimated operator is obtained on the generalized context of q -Boehmians. On top of that, several results and q -Mellin spaces of q -Boehmians are discussed. Furthermore, certain continuous q -embeddings and an inversion formula are also discussed.

Estimates and properties of certain q-Mellin transform on generalized q-calculus theory