scholarly journals STARLIKENESS AND SCHWARZIAN DERIVATIVES OF HIGHER ORDER OF ANALYTIC FUNCTIONS

2017 ◽  
Vol 32 (1) ◽  
pp. 93-106 ◽  
Author(s):  
Ohsang Kwon ◽  
Youngjae Sim
Keyword(s):  
Analytic Functions ◽  
Higher Order ◽  
Schwarzian Derivatives ◽  
Derivatives Of

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 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>

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.

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

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