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Displaying similar documents to “On a class of starlike functions defined in a halfplane”

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.

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

Richard Fournier (1995)

Banach Center Publications

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The problem of estimating the radius of starlikeness of various classes of close-to-convex functions has attracted a certain number of mathematicians involved in geometric function theory ([7], volume 2, chapter 13). Lewandowski [11] has shown that normalized close-to-convex functions are starlike in the disc | z | < 4 √ 2 - 5 . Krzyż [10] gave an example of a function f ( z ) = z + ∑ n = 2 ∞ a n z n , non-starlike in the unit disc , and belonging to the class H = f | f’() lies in the right half-plane. More generally let H* = f |...

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 + ∑ k = 1 ∞ 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 ) ⊆ 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.