On a class of analytic functions associated to a complex domain concerning q-differential-difference operator

Abstract

Abstract In our current investigation, we apply the idea of quantum calculus and the convolution product to amend a generalized Salagean q-differential operator. By considering the new operator and the typical version of the Janowski function, we designate definite new classes of analytic functions in the open unit disk. Significant properties of these modules are considered, and recurrent sharp consequences and geometric illustrations are realized. Applications are considered to find the existence of solutions of a new class of q-Briot–Bouquet differential equations.

Keywords

• Univalent function
• Differential operator
• Unit disk
• Analytic function
• Fractional calculus
• q-calculus