On a Subclass of Analytic Functions Related to a Hyperbola

Jagannath Patel,Ashok Kumar Sahoo

doi:10.1155/2014/570361

Jagannath Patel, Ashok Kumar Sahoo

Open Access

https://doi.org/10.1155/2014/570361

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Abstract

The object of the present investigation is to solve Fekete-Szegö problem and determine the sharp upper bound to the second Hankel determinant for a new classℛ̃(a,c,ρ)of analytic functions in the unit disk. We also obtain a sufficient condition for an analytic function to be in this class.

Highlights

Introduction and PreliminariesLet A be the class of functions f of the form: ∞f (z) = z + ∑anzn (1)n=2 which are analytic in the open unit disk U = {z ∈ C : |z| < 1}
F (z) = z + ∑anzn n=2 which are analytic in the open unit disk U = {z ∈ C : |z| < 1}
Let P denote the class of analytic functions of the form: φ (z) = 1 + p1z + p2z2 + ⋅ ⋅ ⋅ (z ∈ U)

Summary

Introduction

Let A be the class of functions f of the form: A function f ∈ A is said to in the class R(ρ), if it satisfies the inequality: Re {f󸀠 (z)} > ρ (0 ≤ ρ < 1; z ∈ U) . Let P denote the class of analytic functions of the form: φ (z) = 1 + p1z + p2z2 + ⋅ ⋅ ⋅ (z ∈ U) A function f ∈ A is said to be in the class R(a, c, ρ), if it satisfies the following subordination relation: L (a, c) f (z) z

Results

Conclusion