Abstract
In this paper, our goal is to determine sufficient conditions for the family of Struve functions in order to belong to the classes of uniformly convex functions and uniformly starlike functions in the open unit disk U. Several corollaries and consequences of our main results are also derived.
Highlights
Introduction and DefinitionsLet A be the class of functions f (z) of the form: ∞∑ f (z)= z + an zn (1)n=2 which are analytic in the open unit diskU = {z : z ∈C and z
∑ f (z)= z + an zn n=2 which are analytic in the open unit disk
It is well known that the Theory of Special Functions play an important role in Geometric Function Theory, especially in the solution by de Branges [2] of the famous Bieberbachconjecture
Summary
Let A be the class of functions f (z) of the form: We recall here the Struve function of order p [11,12], denoted by Hp (z) and given by H p (z) following Silverman [1], we denote by T the subclass of A consisting of functions of the form: Which is a particular solution of the following second-order nonhomogeneous differential equation: for functions f € A given by (1) and g € A given by
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