Coefficient Inequalities for Certain Univalent Analytic Starlike And Convex Functions in Leaf Like Domain Through Jackson Q-Derivative Operator

Two subclasses of starlike and convex functions analytic in the unit open disk using q-derivative operator have been investigated in the present paper. The necessary and sufficient condition for the function belonging to these classes have been obtained. We further examine various properties, such as the Hadamard product and the quasi-Hadamard product. The coefficient estimates for the function belonging to these classes are also found.

Mathematics Subject Classification 2020: 30C45, 30C50

Starlike, Convex, Hadamard product (or convolution), quasi-Hadamard product, Subordination, , q-derivative operator.

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