2014•AIP conference proceedingsRequires access

Coefficient bounds for a subclass of tilted univalent functions

Nur Hazwani Aqilah Abdul Wahid, Daud Mohamad, Shaharuddin Cik Soh

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Abstract

Let Sα*(ω,δ,A,B) be the class of functions which are analytic and univalent in an open unit disc of the form f(z) = (z−ω)+ ∑ n = 2∞an(z−ω)n and normalized with f(ω) = 0 and f′(ω)−1 = 0 where ω is a fixed point in E and satisfy (eiα(z−ω)f′(z)f(z)−δ−isinα)1cosα−δ = 1+Aφ(z)1+Bφ(z),φ∈Ω(ω) where cosα > δ and |α|<π2. The aim of this paper is to obtain the coefficient bounds for this class of functions. The results generalize some known existing results in the literature.

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What this paper is about

Let Sα*(ω,δ,A,B) be the class of functions which are analytic and univalent in an open unit disc of the form f(z) = (z−ω)+ ∑ n = 2∞an(z−ω)n and normalized with f(ω) = 0 and f′(ω)−1 = 0 where ω is a fixed point in E and satisfy (eiα(z−ω)f′(z)f(z)−δ−isinα)1cosα−δ = 1+Aφ(z)1+Bφ(z),φ∈Ω(ω) where cosα > δ and |α|<π2. The aim of this paper is to obtain the coefficient bounds for this class of functions. The results generalize some known existing results in the literature.

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Available abstract

Let Sα*(ω,δ,A,B) be the class of functions which are analytic and univalent in an open unit disc of the form f(z) = (z−ω)+ ∑ n = 2∞an(z−ω)n and normalized with f(ω) = 0 and f′(ω)−1 = 0 where ω is a fixed point in E and satisfy (eiα(z−ω)f′(z)f(z)−δ−isinα)1cosα−δ = 1+Aφ(z)1+Bφ(z),φ∈Ω(ω) where cosα > δ and |α|<π2. The aim of this paper is to obtain the coefficient bounds for this class of functions. The results generalize some known existing results in the literature.

Key concepts: Subclass, Class (philosophy), Mathematics, Combinatorics, Unit (ring theory), Point (geometry), Analytic function, Discrete mathematics

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