Abstract
We consider a general integral operator and the class of analytic functions. We extend some univalent conditions of Becker's type for analytic functions using a general integral transform.
Highlights
Let ᐁ = {z ∈ C, |z| < 1} be the unit disk, let Ꮽ denote the class of the functions f of the form f (z) = z + a2z2 + a3z3 + · · ·, z ∈ ᐁ, (1.1)
Which are analytic in the open disk, and let ᐁ satisfy the condition f (0) = f (0) − 1 = 0
Let the function f ∈ Ꮽ satisfy the condition (1.4), and let β be a real number, β ≥ 3/|α| and c is a complex number
Summary
Let ᐁ = {z ∈ C, |z| < 1} be the unit disk, let Ꮽ denote the class of the functions f of the form f (z) = z + a2z2 + a3z3 + · · · , z ∈ ᐁ ,. Which are analytic in the open disk, and let ᐁ satisfy the condition f (0) = f (0) − 1 = 0. Consider = { f ∈ Ꮽ : f is univalent functions in ᐁ}. In [1], Pescar needs the following theorem. Let c and β be complex numbers with Re β > 0, |c|≤1, and c= − 1, and let h(z) = z + a2z2 + · · · be a regular function in ᐁ.If c|z|2β +.
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