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6 papers
Coefficients and Integral Mean Estimates for -Quasiconformal Harmonic Mappings
Jasbir Parashar, Saminathan Ponnusamy, A. Sairam Kaliraj
Recently, Li and Ponnusamy~\cite{LiPonnusamy2025} established the coefficient conjecture proposed by Wang et al.~\cite{Wang2024} for several prominent geometric subclasses of $\mat…
Riesz-Fejér inequalities for harmonic functions
Ilgiz R Kayumov, Saminathan Ponnusamy, Anbareeswaran Sairam Kaliraj
In this article, we prove the Riesz - Fejér inequality for complex-valued harmonic functions in the harmonic Hardy space for all . The result is sharp for $p \in…
Injectivity of sections of close-to-convex harmonic mappings with convex analytic part
Anbareeswaran Sairam Kaliraj
In this article, we determine two point distortion theorem and sharp coefficient estimates for the families of close-to-convex harmonic mappings whose analytic part is a convex fun…
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…
On the coefficient conjecture of Clunie and Sheil-Small on Univalent Harmonic Mappings
S. Ponnusamy, A. Sairam Kaliraj
In this paper, we first prove the coefficient conjecture of Clunie and Sheil-Small for a class of univalent harmonic functions which includes functions convex in some direction. Ne…