scholarly journals Estimate for Schwarzian derivative of certain close-to-convex functions

2021 ◽  
Vol 6 (10) ◽  
pp. 10778-10788
Author(s):  
Zhenyong Hu ◽  
◽  
Xiaoyuan Wang ◽  
Jinhua Fan ◽  
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Schwarzian Derivative ◽  
Higher Order ◽  
Schwarzian Derivatives ◽  
Derivatives Of

<abstract><p>Let $ f(z) $ be analytic in the unit disk with $ f(0) = f'(0)-1 = 0 $. For the following close-to-convex subclasses: $ \Re \{(1-z)f'(z)\} &gt; 0, $ $ \Re \{(1-z^{2})f'(z)\} &gt; 0, $ $ \Re \{(1-z+z^{2})f'(z)\} &gt; 0 $ and $ \Re \{(1-z)^{2}f'(z)\} &gt; 0 $, we investigate the bounds for the first two consecutive derivatives of higher order Schwarzian derivatives of $ f(z) $.</p></abstract>

scholarly journals Carleson Measure of Harmonic Schwarzian Derivatives Associated with a Finitely Generated Fuchsian Group of the Second Kind

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Guangming Hu ◽  
Yutong Liu ◽  
Yu Sun ◽  
Xinjie Qian
Keyword(s):  
Harmonic Function ◽  
Unit Disk ◽  
Fuchsian Group ◽  
Fundamental Domain ◽  
Carleson Measure ◽  
Schwarzian Derivative ◽  
Finitely Generated ◽  
Schwarzian Derivatives ◽  
Carleson Condition

Let S H f be the Schwarzian derivative of a univalent harmonic function f in the unit disk D , compatible with a finitely generated Fuchsian group G of the second kind. We show that if S H f 2 1 − z 2 3 d x d y satisfies the Carleson condition on the infinite boundary of the Dirichlet fundamental domain F of G , then S H f 2 1 − z 2 3 d x d y is a Carleson measure in D .

scholarly journals Invariant Schwarzian Derivatives of Higher Order

2010 ◽  
Vol 5 (3) ◽  
pp. 659-670 ◽  
Author(s):  
Seong-A Kim ◽  
Toshiyuki Sugawa
Keyword(s):  
Higher Order ◽  
Schwarzian Derivatives ◽  
Derivatives Of

scholarly journals NORM ESTIMATES OF THE PRE-SCHWARZIAN DERIVATIVES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS

2006 ◽  
Vol 49 (1) ◽  
pp. 131-143 ◽  
Author(s):  
Yong Chan Kim ◽  
Toshiyuki Sugawa
Keyword(s):  
Hardy Spaces ◽  
Convex Functions ◽  
Maximal Operator ◽  
Univalent Functions ◽  
Independent Interest ◽  
Norm Estimates ◽  
Norm Estimate ◽  
Schwarzian Derivatives ◽  
Derivatives Of

AbstractA sharp norm estimate will be given to the pre-Schwarzian derivatives of close-to-convex functions of specified type. In order to show the sharpness, we introduce a kind of maximal operator which may be of independent interest. We also discuss a relation between the subclasses of close-to-convex functions and the Hardy spaces.

scholarly journals Sharp Bounds on the Higher Order Schwarzian Derivatives for Janowski Classes

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 348
Author(s):  
Nak Cho ◽  
Virendra Kumar ◽  
V. Ravichandran
Keyword(s):  
Convex Functions ◽  
Univalent Functions ◽  
Higher Order ◽  
Sharp Bounds ◽  
Schwarzian Derivatives

Higher order Schwarzian derivatives for normalized univalent functions were first considered by Schippers, and those of convex functions were considered by Dorff and Szynal. In the present investigation, higher order Schwarzian derivatives for the Janowski star-like and convex functions are considered, and sharp bounds for the first three consecutive derivatives are investigated. The results obtained in this paper generalize several existing results in this direction.

On sandwich theorems for higher-order derivatives of multivalent analytic functions associated with the generalized Noor integral operator

2015 ◽  
Vol 08 (01) ◽  
pp. 1450024 ◽  
Author(s):  
Abbas Kareem Wanas
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Higher Order ◽  
Open Unit ◽  
Open Unit Disk ◽  
Derivatives Of

In this paper, we obtain some subordination and superordination results for higher-order derivatives of multivalent analytic functions in the open unit disk by generalized Noor integral operator. These results are applied to obtain sandwich results. Our results extend corresponding previously known results.

Coefficient and pre-Schwarzian norm estimates for a class of generalized doubly close-to-convex functions

2014 ◽  
Vol 25 (10) ◽  
pp. 1450094
Author(s):  
Dorina Răducanu
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Coefficient Bounds ◽  
Norm Estimates ◽  
New Class ◽  
Schwarzian Derivatives ◽  
Derivatives Of

In this paper, we consider a new class 𝒞(ϕ, ψ, η) of analytic functions defined by means of subordination. Coefficient bounds, Fekete–Szegö problem and norm estimates of the pre-Schwarzian derivatives of functions belonging to the class 𝒞(ϕ, ψ, η) are investigated. A class of multiple close-to-convex functions is also considered.

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

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