Bohr--Rogosinski radius for analytic functions

By Ilgiz R. Kayumov, Saminathan Ponnusamy. 2017

58 citations recorded by the source corpus.

There are a number of articles which deal with Bohr's phenomenon whereas only a few papers appeared in the literature on Rogosinski's radii for analytic functions defined on the unit disk $|z|<1$. In this article, we introduce and investigate Bohr-Rogosinski's radii for analytic functions defined for $|z|<1$. Also, we prove several different improved versions of the classical Bohr's inequality. Finally, we also discuss the Bohr-Rogosinski's radius for a class of subordinations. All the results are proved to be sharp.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5fb8fc674b9ed4a7ea59888639a9fd5316da10ca

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In Applied Mathematics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Sharp Bohr type inequality (2020, methodology): “oughout this paper Sr(f) denotes the area of the image of the subdisk |z| <runder the mapping fand when there is no confusion, we let for brevity Sr for Sr(f). More recently, Kayumov and Ponnusamy [29] improved Bohr’s inequality (1) in various forms. For example, the following inequality is obtai”
Improved Bohr’s inequality for locally univalent harmonic mappings (2017, background): “ns of Bohr’s inequality for the harmonic mappings of the form f = h+g, where h is bounded by 1 and |g′(z)| ≤ |h′(z)|. The improvementsareobtainedalongthelinesofanearlierworkofKayumovandPonnusamy, i.e.[9],forexampleatermrelatedtotheareaoftheimageofthediskD(0,r)underthe mapping f is considered. Our re”
Refined Bohr inequality for bounded analytic functions (2020, background): “e results, there are plenty of works about Bohr inequality for the family B. Based on the notion of Rogosinski’s inequality and Rogosinski’s radius investigated in [23, 31, 33], Kayumov and Ponnusamy [22] introduced and obtained the following Bohr-Rogosinski inequality and Bohr-Rogosinski radius. Th”