7 papers
Stable classes of harmonic mappings
Gang Liu, Saminathan Ponnusamy, Victor V. Starkov
Let denote the set of all sense-preserving harmonic mappings in the unit disk $\ID$, normalized with and . In this p…
The Jacobian conjecture and injectivity conditions
Saminathan Ponnusamy, Victor V. Starkov
One of the aims of this article is to provide a class of polynomial mappings for which the Jacobian conjecture is true. Also, we state and prove several global univalence theorems…
Coefficients of univalent harmonic mappings
Saminathan Ponnusamy, Anbareeswaran Sairam Kaliraj, Victor V. Starkov
Let denote the class of all functions that are sense-preserving, harmo…
Sections of univalent harmonic mappings
Saminathan Ponnusamy, Anbareeswaran Sairam Kaliraj, Victor V. Starkov
In this article, we determine the radius of univalence of sections of normalized univalent harmonic mappings for which the range is convex (resp. starlike, close-to-convex, convex…
Absolutely Convex, Uniformly Starlike and Uniformly Convex Harmonic Mappings
Saminathan Ponnusamy, Anbareeswaran Sairam Kaliraj, Victor V. Starkov
In this paper, we prove necessary and sufficient conditions for a sense-preserving harmonic function to be absolutely convex in the open unit disk. We also estimate the coefficient…
Univalence criterion for harmonic mappings and -like functions
Sergey Yu. Graf, Saminathan Ponnusamy, Victor V. Starkov
In this paper, we obtain a new characterization for univalent harmonic mappings and obtain a structural formula for the associated function which defines the analytic -like func…