Displaying similar documents to “On Some Results for l a m b d a -spirallike and l a m b d a -robertson Functions of Complex Order”

A Note on Univalent Functions with Finitely many Coefficients

Darus, M., Ibrahim, R. (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 30C45 The main object of this article is to introduce sufficient conditions of univalency for a class of analytic functions with finitely many coefficients defined by approximate functions due to Suffridge on the unit disk of the complex plane whose image is saddle-shaped. Sandwich theorem is also discussed.

Integral representations of bounded starlike functions

Frode Rønning (1995)

Annales Polonici Mathematici

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For α ≥ 0 let α denote the class of functions defined for |z| < 1 by integrating 1 / ( 1 - x z ) α if α > 0, and log(1/(1-xz)) if α = 0, against a complex measure on |x| = 1. We study families of starlike functions where zf’(z)/f(z) ranges over a parabola with given focus and vertex. We prove a number of properties of these functions, among others that they are bounded and that they belong to 0 . In general, it is only known that bounded starlike functions belong to α for α > 0.