25 citations · 40 across the 12 of their papers we have counts for
18 papers
Bernstein-type inequalities for mean -valent functions
Anton Baranov, Ilgiz Kayumov, Rachid Zarouf
We derive new integral estimates of the derivatives of mean -valent functions in the unit disk. Our results develop and complement estimates obtained by E.P. Dolzhenko and A.A.…
Analytic capacities in Besov spaces
Anton Baranov, Michael Hartz, Ilgiz Kayumov +1
We derive new estimates on analytic capacities of finite sequences in the unit disc in Besov spaces with zero smoothness, which sharpen the estimates obtained by N.K.Nikolski in 20…
Weissler and Bernoulli type inequalities in Bergman spaces
Anton D. Baranov, Ilgiz R. Kayumov, Diana M. Khammatova +1
We consider Weissler type inequalities for Bergman spaces with general radial weights and give conditions on the weight in terms of its moments ensuring that $\|f_r\|_{A^{2n}(w…
On Bloch seminorm of finite Blaschke products in the unit disk
Anton D. Baranov, Ilgiz R. Kayumov, Semen R. Nasyrov
We prove that, for any finite Blaschke product in the unit disk, the corresponding Riemann surface over the --plane contains a one-sheeted disk of the radius . Mor…
The Bohr inequality for the generalized C{é}saro averaging operators
Ilgiz R Kayumov, Diana M. Khammatova, Saminathan Ponnusamy
The main aim of this paper is to prove a generalization of the classical Bohr theorem and as an application, we obtain a counterpart of Bohr theorem for the generalized Cesáro oper…
Bohr--Rogosinski inequalities for bounded analytic functions
Seraj A. Alkhaleefah, Ilgiz R. Kayumov, Saminathan Ponnusamy
In this paper we first consider another version of the Rogosinski inequality for analytic functions in the unit disk , in which we replace…
Sharp Bohr type inequality
Amir Ismagilov, Ilgiz R Kayumov, Saminathan Ponnusamy
This article is devoted to the sharp improvement of the classical Bohr inequality for bounded analytic functions defined on the unit disk. We also prove two other sharp versions of…
On a conjecture about univalent polynomials
Ilgiz R. Kayumov, Diana M. Khammatova
In this paper we prove a recent conjecture formulated by Dmitrishin, Smorodin and Stokolos about that certain polynomials are univalent in the unit disk. As a consequence we get an…
On the sum of squares of the coefficients of Bloch functions
I. R. Kayumov, K. -J. Wirths
In this article several types of inequalities for weighted sums of the moduli of Taylor coefficients for Bloch functions are proved
On the Bohr inequality with a fixed zero coefficient
Seraj A. Alkhaleefah, Ilgiz R Kayumov, Saminathan Ponnusamy
In this paper, we introduce the study of the Bohr phenomenon for a quasi-subordination family of functions, and establish the classical Bohr's inequality for the class of quasisubo…
Riesz-Fejér inequalities for harmonic functions
Ilgiz R Kayumov, Saminathan Ponnusamy, Anbareeswaran Sairam Kaliraj
In this article, we prove the Riesz - Fejér inequality for complex-valued harmonic functions in the harmonic Hardy space for all . The result is sharp for $p \in…
On a powered Bohr inequality
Ilgiz R Kayumov, Saminathan Ponnusamy
The object of this paper is to study the powered Bohr radius , , of analytic functions and such that defined on the u…
Bohr radius for locally univalent harmonic mappings
Ilgiz R Kayumov, Saminathan Ponnusamy, Nail Shakirov
We consider the class of all sense-preserving harmonic mappings of the unit disk $\ID$, where and are analytic with , and determine the Bohr rad…
Bohr--Rogosinski radius for analytic functions
Ilgiz R Kayumov, Saminathan Ponnusamy
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 un…
Bohr's inequality for analytic functions and harmonic functions
Ilgiz R Kayumov, Saminathan Ponnusamy
We determine the Bohr radius for the class of all functions of the form analytic in the unit disk and satisfy the condition $…
Bohr inequality for odd analytic functions
Ilgiz R Kayumov, Saminathan Ponnusamy
We determine the Bohr radius for the class of odd functions satisfying for all , settling the recent conjecture of Ali, Barnard and Solynin \cite{AliBarSol…
Makarov's principle for the Bloch unit ball
Oleg Ivrii, Ilgiz Kayumov
Makarov's principle relates three characteristics of Bloch functions that resemble the variance of a Gaussian: asymptotic variance, the constant in Makarov's law of iterated logari…
Exact analytical solution for one nonlinear variational problem of the cavitation theory
D. V. Maklakov, I. R. Kayumov
In this paper we investigate the limiting values of the lift and drag coefficients of profiles in the Helmholtz--Kirchhoff (infinite cavity) flow. The coefficients are based on the…