On the radius of univalence of a polynomial

Mathematische Zeitschrift -     

The zeros of the complementary error function

We show that the complementary error function, $\text{erfc} (z)= \frac{2}{\sqrt{\pi}}\int_z^{\infty}{e^{-s^2} \text{d}s}$ , has no zeros in $\text{D}= \left\{ z : \frac{3}{4} \ \pi \le Arg z \le\frac{5}{4} \ \pi \right\}$ .     

The theory of sharp first-order univalence criteria

A condition of the formf′ (D) ⊂R is calleda first-order univalence criterion if all functions for which it holds are univalent inD. By means of a careful analysis of the behavior of the corresponding extremal functions, we establish fundamental principles for a coherent theory of sharp criteria of this kind. In particular, we examine the relationship between three different concepts of sharpness and show how large classes of first-order univalence criteria which are sharp in a strong sense may be described in terms of the univalence properties of families of analytic functions depending on a finite number of parameters. This research was supported in part by the Chilean government through FONDECYT grant No. 0809-91.     

On the univalence of the log-biharmonic mappings

In this paper, we establish the univalence and starlikeness connection between log-biharmonic mappings and logharmonic mappings.     

On the univalence of an integral operator

In this work the author introduces a general integral operator and determines conditions for the univalence of this integral operator.     

On the angular derivative and univalence

f . , , — , A f f(). , , f() 0 . , , ,A , f . , f() - f() . , , . (1976) ( ¦f(z)¦<1) . . (1969) ( ).     

On the Radii of univalence of Gel'fond-Leont'ev derivatives

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 390–399, March, 1995.     

On some criteria for the univalence of analytic functions

Criteria for the univalence of functions f(z) which are regular in the domain ¦z¦ < 1 are obtained in the form of restrictions on the modulus of the quotient f (z) [f '(z)]^–1. Analogous results are obtained also for functions which are analytic in the interior of the unit disk except for a simple pole at infinity.Translated from Matematicheskie Zametki, Vol. 13, No. 3, pp. 359–366, March, 1973.In conclusion the author wishes to thank L. A. Aksent'ev and F. G. Avkhadiev for discussion of the results and valuable remarks.     

On the univalence of functions with logharmonic laplacian

In this paper, we prove Radó’s theorem holds for functions of the form is logharmonic. We show that if F is of the form , where is logharmonic, then F is starlike iff ψ(z)=h(z)/g(z) is starlike. In addition, when , where L is logharmonic and H is harmonic, we give the sufficient conditions for F to be locally univalent.     

Sufficient conditions for the univalence of quasiconformal mappings

Using two methods, quasiconformal continuation involving a theorem of Hadamard and direct estimation of f(z₂)?f(z₁), we obtain sufficient conditions for the univalence of continuously differentiable mappings f(z) of plane domains which, in the case of conformal mappings, reduce to both well-known and new results.