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Radius problems for univalent functions

Sokół Janusz, Trąbka-Więcław Katarzyna

Journal of Applied Analysis

2020

Vol. 26, nr 1

111--115

This paper considers the following problem: for what value r, r < 1 a function that is univalent in the unit disk |z| < 1 and convex in the disk |z| < r becomes starlike in |z| < 1. The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered.

On complex mappings harmonic in the unit disc with some coefficient conditions

Łazińska Anna

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2002

z. 26 [199]

107-116

Let h = u + w, where u,v are real harmonic functions in the unit disc delta. Such functions are called complex mappings harmonic in delta. The function h may be written in the form h = f + g, where f, g are functions holomorphic in the unit disc, of course. Studies of complex harmonic functions were initiated in 1984 by J. Clunie and T. Sheil-Small ([CS-S]) and were continued by many others mathematicians. We can find some papers on functions harmonic in delta, satisfying certain coefficient conditions, e.g. [AZ], [S], [G]. We investigate some more general problems, which appeared during the seminar conducted by Professor Z. Jakubowski.

On some subclass of strongly starlike functions

Sokół J.

Demonstratio Mathematica

1998

Vol. 31, nr 1

81-86