Abstract
In this paper, we introduce and study some properties of unified class WTλ(Φ,Ψ;η,β,p) involving the Hadamard Products given by Juneja et. al in 1985. The properties include coefficient bounds, growth and distortion, and closure theorem. Further, the radii of starlikeness and convexity is also given. AMS Subj. Classification: 30C45.
Highlights
Introduction and PreliminariesDenote by A( p) the class of functions of the form ∞∑ f (z) = z + ap+k z p+k k =1 (1.1)which are analytic in the open disc U = {z : z ∈ C and z < 1}
Which are analytic in the open disc U = {z : z ∈ C and z < 1}
The class of uniformly convex and uniformly starlike functions has been extensively studied by Goodman[1,2], Ma and Minda[3]
Summary
Denote by A( p) the class of functions of the form Denote by S* ( p,α) the class of starlike functions f ∈ A( p) of order α (0 ≤ α < p) satisfying M. Darus / Journal of Fundamental Sciences 1 (2005) 16-22 and let C( p,α ) be the class of convex functions f ∈ A( p) of order α (0 ≤ α < p) such that zf ' ∈ S* ( p,α ) . A function f ∈ A(1) is said to be in the class of β -uniformly convex functions of order α , denoted by β −UCV (α ) [4, 5] if
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