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In this paper, we define convolutions (f ∗g([α]))(z) and (f ∗h([α]))(z) of functions analytic in the open unit disk with some non-zero parameter α, satisfying certain recurring relations. Making use of admissible function method introduced by Miller and Mocanu, certain geometric properties of these convolutions are obtained. Taking specific forms of the functions g([α]) and h([α]), some consequences of our results are also given.

Certain geometric properties of analytic functions associated with the convolutions