Skip to content
DSML.KZ
Publications

Article · Bulletin of the National Engineering Academy of the Republic of Kazakhstan · June 30, 2026

Estimation of the logarithmic derivative in the generalized Yanovsky class

Fedor F. Maiyer, Мейрамбек Габдулиевич Тастанов

Fedor Maiyer
Open via DOI

Abstract

We consider the Yanovsky class of functions j(z) of the form j(z) = 1 + cnzn + cn+1zn+1 + …, n ≥ 1 regular in a disk E and subordinate to the function j(z) = (1 + Az)/(1 + Bz), where –1 ≤ B < A ≤ 1, that is, j(0) = 1 and j(E)  j0(E). The article finds an exact estimate for the absolute value of the logarithmic derivative |j(z)/j(z)| in this class of functions and examines two special cases that, for certain parameter values, lead to a number of well-known results.

Analytic and geometric function theoryHolomorphic and Operator TheoryMeromorphic and Entire Functionslogarithmic derivativeanalytic functions in the unit disksubordination

More by Fedor Maiyer