Boundary Schwarz inequalities arising from Rogosinski's lemma

@article{Mercer2018BoundarySI,
  title={Boundary Schwarz inequalities arising from Rogosinski's lemma},
  author={Peter R. Mercer},
  journal={Journal of Classical Analysis},
  year={2018},
  pages={93-97}
}
We consider some Schwarz and Carathéodory inequalities at the boundary, as consequences of a lemma due to Rogosinski. 

Some remarks on the Subordination Principle for analytic functions concerned with Rogosinski's lemma

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the

Estimates for -spirallike function of complex order on the boundary

  • T. Akyel
  • Mathematics
    Ukrains’kyi Matematychnyi Zhurnal
  • 2022
UDC 517.5 We give some results for -spirallike function of complex order at the boundary of the unit disc . The sharpness of these results is also proved. Furthermore, three examples for our results

Sharpened forms of analytic functions concerned with Hankel determinant

In this paper, we present a Schwarz lemma at the boundary for analytic functions at the unit disc, which generalizes classical Schwarz lemma for bounded analytic functions. For new inequalities, the

Sharpened forms for λ-spirallike function of complex order on the boundary

We present a different version of Schwarz Lemma and estimate the angular derivative of the function zf′(z)f(z) from below for λ−spirallike function f (z) of complex order at the boundary of the unit

Upper bound of Hankel determinant for a class of analytic functions

The aim of this study is to solve the Fekete-Szeg? problem and to define upper bound for Hankel determinant H2(1) in a novel class K of analytical functions in the unit disc. Moreover, in a class

A sharp Carathéodory's inequality on the right half plane

  • B. Örnek
  • Mathematics
    Journal of Classical Analysis
  • 2019
. In this paper, a boundary version of Carath´eodory’s inequality on the right half plane is investigated. Here, the function Z ( s ) , is given as Z ( s ) = 1 + c 1 ( s − 1 )+ c 2 ( s − 1 ) 2 + ...

Estimates for analytic functions concerned with Hankel determinant

  • B. Örnek
  • Mathematics
    Ukrains’kyi Matematychnyi Zhurnal
  • 2021
UDC 517.5 We give an upper bound of Hankel determinant of the first order for the classes of an analytic function. In addition, an evaluation with the Hankel determinant from below will be given for

SOME RESULTS CONCERNED WITH HANKEL DETERMINANT FOR N (α) CLASS

In this paper, we give some results an upper bound of Hankel determinant of H2(1) for the classes of N (α). We get a sharp upper bound for H2(1) = c3−c2 for N (α) by adding z1, z2, . . . , zn zeros

Some remarks on rotation theorems for complex polynomials

  • V. Dubinin
  • Mathematics, Philosophy
    Sibirskie Elektronnye Matematicheskie Izvestiya
  • 2021
For any complex polynomial P (z) = c0+c1z+...+cnz , cn 6= 0, having all its zeros in the unit disk |z| ≤ 1, we consider the behavior of the function (argP (e))θ when the real argument θ changes. We

Bounds of Hankel determinants for analytic function

In this paper, we give estimates of the Hankel determinant $H_{2}(1)$ in a novel class $\mathcal{N}\left( \varepsilon \right) $ of analytical functions in the unit disc. In addition, the relation

References

SHOWING 1-10 OF 10 REFERENCES

CARATHÉODORY'S INEQUALITY ON THE BOUNDARY

In this paper, a boundary version of Carathéodory’s inequality is investigated. Also, new inequalities of the Carathéodory’s inequality at boundary are obtained and the sharpness of these

Sharpened Versions of the Schwarz Lemma

Abstract We prove a version of the Schwarz Lemma in which the images of two points are known. Two classical results (due to Dieudonne and Rogosinski) are simple corollaries.

Invitation to complex analysis

Preface 1. From complex numbers to Cauchy's Theorem 2. Applications of Cauchy's Theorem 3. Analytic continuation 4. Harmonic functions and conformal mapping 5. Miscellaneous topics Index.

The Schwarz Inequality on the Boundary for Functions Regular in the Disk

The classical Schwarz inequality on the boundary of the disk for the functions regular in the disk is refined in various directions. Inequalities involving zeros of the function, an inequality for

Boundary Schwarz lemma for holomorphic functions

In this paper, a boundary version of Schwarz lemma is investigated. We take into consideration a function f (z) holomorphic in the unit disc and f (0) = 0 such that ∣∣∣< f ∣∣∣ < 1 for |z| < 1, we

A sharp Schwarz inequality on the boundary

A number of classical results reflect the fact that if a holomorphic function maps the unit disk into itself, taking the origin into the origin, and if some boundary point b maps to the boundary,

ÖRNEK AND B. GÖK, Boundary Schwarz lemma for holomorphic functions, Filomat

  • 2017

ÖRNEK, The Carathéodory inequality on the boundary for holomorphic functions in the unit disk

  • J. Math. Physics, Analysis, Geometry
  • 2016

DUREN, Univalent Functions, Springer-Verlag

  • New York & Berlin,
  • 1983