# 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.

## 17 Citations

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

- Mathematics
- 2021

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

- MathematicsUkrains’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

- Mathematics
- 2019

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

- Mathematics
- 2021

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

- MathematicsFilomat
- 2021

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

- MathematicsJournal 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

- MathematicsUkrains’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

- Mathematics
- 2021

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

- Mathematics, PhilosophySibirskie 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

- Mathematics
- 2020

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…

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