2016/05/07 by Saminathan Ponnusamy, Anbareeswaran Sairam Kaliraj, Ponnusamy, Saminathan +3
Mathematics · #30C45 #30C50 #30C55 #30C80 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Primary:31A05 #Secondary: 33C05
paper · pdf · doi:10.48550/arxiv.1605.02171
openalex publication_date 2016/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove necessary and sufficient conditions for a\nsense-preserving harmonic function to be absolutely convex in the open unit\ndisk. We also estimate the coefficient bound and obtain growth, covering and\narea theorems for absolutely convex harmonic mappings. A natural generalization\nof the classical Bernardi type operator for harmonic functions is considered\nand its connection between certain classes of uniformly starlike harmonic\nfunctions and uniformly convex harmonic functions is also investigated. At the\nend, as applications, we present a number of results connected with\nhypergeometric and polylogarithm functions.\n