First-order univalence criteria, interior chord-arc conditions and quasidisks

Sufficient conditions for univalence and starlikeness

It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|

Univalence conditions and Sturm-Liouville eigenvalues

Univalence criteria for general integral operator

Let A be the class of all analytic functions which are analytic in the open unit disc U = {z : |z| < 1} and Gb = { f ∈ A : ∣∣∣∣ 1 + zf ′′(z)/f ′(z) zf ′(z)/f(z) − 1 ∣∣∣∣ < b, z ∈ U } . In this paper, we derive sufficient conditions for the integral operator Ii γ (f1, ..., fn)(z) =    z ∫ 0 tγ−1 ( f ′ 1(t) )α1 ( f1(t) t )1−α1 ... ( f ′ n(t) )αn ( fn(t) t )1−αn dt    1 γ to be analytic and ...

Some Sufficient Conditions for Univalence

A new subclass R(u), 0 < u < I, of the class St(I/2) the class of starlike functions of order I/2 is introduced and it is shown that R(u) is closed with respect to the Hadamard product of analytic functions. Some sufficient conditions for the normalized regular functions to be univalent in the unit disk E are given.

New univalence criteria for some integral operators

In this work we consider some integral operators for analytic functions in the open unit disk and we obtain new univalence criteria for these integral operators, using Mocanu’s and Şerb’s Lemma, Pascu’s Lemma. Mathematics Subject Classification (2010): 30C45.