Bohr--Rogosinski inequalities for bounded analytic functions

2020/04/19 by Alkhaleefah, Seraj A., Kayumov, Ilgiz R., Ponnusamy, Saminathan · 2 citations
#30B10 #30C62 #30H05 #31A05 #40A30 #41A58 #Complex Variables (math.CV) #FOS: Mathematics #Primary 30A10 #Secondary: 30C75

paper · doi:10.48550/arxiv.2004.08895

Abstract

In this paper we first consider another version of the Rogosinski inequality for analytic functions f(z)=∑_n=0^∞ a_nzⁿ in the unit disk |z| < 1, in which we replace the coefficients a_n (n= 0,1,… ,N) of the power series by the derivatives f⁽ⁿ⁾(z)/n! (n= 0,1,… ,N). Secondly, we obtain improved versions of the classical Bohr inequality and Bohr's inequality for the harmonic mappings of the form f = h + g, where the analytic part h is bounded by 1 and that |g'(z)| ≤ k|h'(z)| in |z| < 1 and for some k ∈ [0,1].

Cited by

• Multidimensional analogues of the refined Bohr type inequalities
• A unified framework for Bohr-type inequalities using multiple Schwarz functions

Related

• The sharp refined Bohr-Rogosinski inequalities for certain classes of harmonic mappings
• Bohr-Rogosinski and improved Bohr type inequalities for certain fully starlike harmonic mappings
• Bohr-Rogosinski Inequalities for bounded analytic functions
• Bohr inequalities for unimodular bounded functions on simply connected domains
• The Bohr's Phenomenon involving multiple Schwarz functions