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Some sufficient conditions for univalence and close-to-convexity

Nunokawa Mamoru, Cho Nak Eun, Kwon Oh Sang, Sokół Janusz

Journal of Applied Analysis

2020

Vol. 26, nr 1

91--95

In the class of analytic functions in the unit disc |z| < 1 we prove some new sufficient conditions for functions to be univalent or to be close-to-convex in the unit disc. Also we extend Ozaki’s condition that Re{exp(iα)f (p)(z)} > 0 in |z| < 1 implies that f(z) is at most p-valent in |z| < 1.

Fekete-Szegö problems for certain class of analytic functions associated with quasi-subordination

Sahoo P.

Journal of Mathematics and Applications

2017

Vol. 40

161--170

In this paper, we determine the coefficient estimates and the Fekete-Szegö inequalities for [wzór], the class of analytic and univalent functions associated with quasi-subordination.

Partial sums of a certain harmonic univalent meromorphic functions

Aouf M. K., El-Ashwah R. M., Dziok J., Stankiewicz J.

Journal of Mathematics and Applications

2014

Vol. 37

5--12

In the present paper we determine sharp lower bounds of the real part of the ratios of harmonic univalent meromorphic functions to their sequences of partial sums [...].

New univalence criterions for special general integral operators

Ebadian A., Sokół J.

Journal of Mathematics and Applications

2013

Vol. 36

63--69

In this work we consider some integral operators on the special subclasses of the set of analytic functions in the unit disc which are defined by the Hadamard product. Using the univalence criterions, we obtain new sucient conditions for these operators to be univalent in the open unit disk. We give some applications of the main results.