ORIGINAL ARTICLE
Improved Bohr inequality for harmonic mappings
Gang Liu,
Saminathan Ponnusamy,
Gang Liu
College of Mathematics and Statistics, Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang Normal University, Hengyang, China
Search for more papers by this authorCorresponding Author
Saminathan Ponnusamy
Department of Mathematics, Indian Institute of Technology Madras, Chennai, India
Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
Correspondence
Saminathan Ponnusamy, Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India.
Email: [email protected]
Search for more papers by this authorGang Liu,
Saminathan Ponnusamy,
Gang Liu
College of Mathematics and Statistics, Hunan Provincial Key Laboratory of Intelligent Information Processing and Application, Hengyang Normal University, Hengyang, China
Search for more papers by this authorCorresponding Author
Saminathan Ponnusamy
Department of Mathematics, Indian Institute of Technology Madras, Chennai, India
Lomonosov Moscow State University, Moscow Center of Fundamental and Applied Mathematics, Moscow, Russia
Correspondence
Saminathan Ponnusamy, Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, India.
Email: [email protected]
Search for more papers by this authorAbstract
In order to improve the classical Bohr inequality, we explain some refined versions for a quasi-subordination family of functions in this paper, one of which is key to build our results. Using these investigations, we establish an improved Bohr inequality with refined Bohr radius under particular conditions for a family of harmonic mappings defined in the unit disk . Along the line of extremal problems concerning the refined Bohr radius, we derive a series of results. Here, the family of harmonic mappings has the form , where , the analytic part h is bounded by 1 and that in and for some .
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