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2007•Unpublished venueRequires access

Convolutions for certain analytic functions

Junichi Nishiwaki, Shigeyoshi Owa

Open publisher page 2 citations

Abstract

Applying the coefficient inequalities of functions f(z) belonging to the subclasses SD(α, β) and KD(α, β) of certain analytic functions in the open unit disk U, two subclasses SD∗(α, β) and KD∗(α, β) are introduced. In this present paper, some interesting convolution properties of functions f(z) in the classes SD∗(α, β) and KD∗(α, β) are discussed by using Shwarz inequality. 2000 Mathematical Subject Classification: 30C45 Key words and phrases: Analytic function, unifomly starlike, uniformly convex, convolution. 1

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What this paper is about

Applying the coefficient inequalities of functions f(z) belonging to the subclasses SD(α, β) and KD(α, β) of certain analytic functions in the open unit disk U, two subclasses SD∗(α, β) and KD∗(α, β) are introduced. In this present paper, some interesting convolution properties of functions f(z) in the classes SD∗(α, β) and KD∗(α, β) are discussed by using Shwarz inequality. 2000 Mathematical Subject Classification: 30C45 Key words and phrases: Analytic function, unifomly starlike, uniformly convex, convolution. 1

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Available abstract

Applying the coefficient inequalities of functions f(z) belonging to the subclasses SD(α, β) and KD(α, β) of certain analytic functions in the open unit disk U, two subclasses SD∗(α, β) and KD∗(α, β) are introduced. In this present paper, some interesting convolution properties of functions f(z) in the classes SD∗(α, β) and KD∗(α, β) are discussed by using Shwarz inequality. 2000 Mathematical Subject Classification: 30C45 Key words and phrases: Analytic function, unifomly starlike, uniformly convex, convolution. 1

Key concepts: Analytic function, Convolution (computer science), Mathematics, Unit disk, Quasi-analytic function, Unit (ring theory), Pure mathematics, Inequality

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