Nehari Type Theorems and Uniform Local Univalence of Harmonic Mappings

The paper is devoted to finding conditions, sufficient for uniform local univalence of sense-preserving mappings, harmonic in the unit disc of the complex plane; the conditions are given in terms of the generalized Schwarzian derivative introduced by R. Hernández and M. J. Martín. The main section contains proofs of the conditions of univalence and uniform local univalence. In the proofs, the methods of the theory of linear-invariant families and generalized Schwarzian derivatives are used. The proved criteria are effective in the case of quasiconformal harmonic mappings; this is confirmed by examples. In the final section, some related methods are applied to harmonic mappings associated with non-parametric minimal surfaces. An estimation of the Gaussian curvature of minimal surfaces is obtained; it is given in the terms of the order of the associated harmonic mapping.

     

Univalence criterion for meromorphic functions and Loewner chains

The object of the present paper is to obtain a more general condition for univalence of meromorphic functions in the U^∗. The significant relationships and relevance with other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results.     

On the starlikeness and convexity of a class of analytic functions

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Injectivity Conditions in the Complex Plane

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Becker type univalence conditions for harmonic mappings

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Univalence conditions of certain integral operators

The purpose of the present paper is to determine univalence conditions of certain integral operators.