On a radius problem concerning a class of close-to-convex functions

Richard Fournier

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Displaying similar documents to “On a radius problem concerning a class of close-to-convex functions”

On certain subclass of close-to-convex functions.

Wang, Zhigang, Gao, Chunyi, Yuan, Shaomou (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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Some Results of Analytic Functions in the Unit Disc

Y. Polatoģlu (2005)

Publications de l'Institut Mathématique

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Starlikeness of functions satisfying a differential inequality

Rosihan M. Ali, S. Ponnusamy, Vikramaditya Singh (1995)

Annales Polonici Mathematici

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In a recent paper Fournier and Ruscheweyh established a theorem related to a certain functional. We extend their result differently, and then use it to obtain a precise upper bound on α so that for f analytic in |z| < 1, f(0) = f'(0) - 1 = 0 and satisfying Re{zf''(z)} > -λ, the function f is starlike.

A study on the generalization of Janowski functions in the unit disc.

Polatoglu, Y., Bolcal, M., Sen, A., Yavuz, E. (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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The Fekete-Szegő theorem for close-to-convex functions of the class $K_{s h} (α, β)$ .

Darus, Maslina (2002)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

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A class of analytic functions defined by Ruscheweyh derivative

K. S. Padmanabhan, M. Jayamala (1991)

Annales Polonici Mathematici

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The function $f (z) = z^{p} + \sum_{k = 1}^{\infty} a_{p + k} z^{p + k}$ (p ∈ ℕ = 1,2,3,...) analytic in the unit disk E is said to be in the class $K_{n, p} (h)$ if ( $D^{n + p} f) / (D^{n + p - 1} f) ≺ h$ , where $D^{n + p - 1} f = (z^{p}) / ({(1 - z)}^{p + n}) * f$ and h is convex univalent in E with h(0) = 1. We study the class $K_{n, p} (h)$ and investigate whether the inclusion relation $K_{n + 1, p} (h) \subseteq K_{n, p} (h)$ holds for p > 1. Some coefficient estimates for the class are also obtained. The class $A_{n, p} (a, h)$ of functions satisfying the condition $a * (D^{n + p} f) / (D^{n + p - 1} f) + (1 - a) * (D^{n + p + 1} f) / (D^{n + p} f) ≺ h$ is also studied.