TL;DR
This paper investigates bounds on the derivative of analytic functions on the unit disc with a finite number of exceptional real values, providing sharp bounds for one exceptional value and analyzing the case of two.
Contribution
It establishes a sharp upper bound for the derivative at zero for functions with one exceptional value and extends analysis to two exceptional values.
Findings
Sharp bound for |f'(0)| when one exceptional value is present
Analysis of the case with two exceptional values
Extension of bounds to multiple exceptional values
Abstract
In this paper we present a result about analytic functions f defined on the open unit disc and with a finite number of exceptional values containedin the real interval (0, 1). We find an upper bound for the modulus of f' in 0. This bound is sharp in the case of one exceptional value. We also analyzed the case of two exceptional values.
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Taxonomy
TopicsAnalytic and geometric function theory · Polymer Synthesis and Characterization