Refinements of the Bohr and Rogosinski phenomena

Article Type

Research Article

Publication Title

Journal of Mathematical Analysis and Applications

Abstract

We obtain improved versions of a classical theorem of Rogosinski concerning the partial sums of a bounded holomorphic function defined on the open unit disk D. Further, we establish refined versions of a generalized Bohr inequality for holomorphic functions mapping D inside a simply connected or convex domain Ω⊊C. In addition, we improve on the classical Bohr inequality for the family of holomorphic self mappings of D and for its subfamily consisting of functions that fix the origin.

DOI

10.1016/j.jmaa.2021.125847

Publication Date

4-1-2022

Comments

Open Access, Bronze

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