Majorization of starlike and convex functions of complex order involving linear operators

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
K. Thilagavathi
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Linear Operators ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractThe main object of this present paper is to investigate the problem of majorization of certain class of analytic functions of complex order defined by the Dziok-Raina linear operator. Moreover we point out some new or known consequences of our main result.

scholarly journals Fekete–Szegö problem for certain subclasses of analytic functions

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Halit Orhan ◽  
Erhan Deniz ◽  
Murat Çağlar
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractIn this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order

scholarly journals Convolution conditions for bounded \(\alpha\)-starlike functions of complex order

2017 ◽  
Vol 71 (1) ◽  
pp. 65
Author(s):  
A. Y. Lashin
Keyword(s):  
Complex Plane ◽  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
General Class ◽  
Starlike Functions ◽  
Starlike And Convex Functions ◽  
Complex Order ◽  
Sălăgean Operator ◽  
Salagean Operator

Let \(A\) be the class of analytic functions in the unit disc \(U\) of the complex plane \(\mathbb{C}\) with the normalization \(f(0)=f^{^{\prime }}(0)-1=0\). We introduce a subclass \(S_{M}^{\ast }(\alpha ,b)\) of \(A\), which unifies the classes of bounded starlike and convex functions of complex order. Making use of Salagean operator, a more general class \(S_{M}^{\ast }(n,\alpha ,b)\) (\(n\geq 0\)) related to \(S_{M}^{\ast }(\alpha ,b)\) is also considered under the same conditions. Among other things, we find convolution conditions for a function \(f\in A\) to belong to the class \(S_{M}^{\ast }(\alpha ,b)\). Several properties of the class \(S_{M}^{\ast }(n,\alpha ,b)\) are investigated.

The Fekete–Szegö functional for generalized starlike and convex functions of complex order

2020 ◽  
pp. 2150036
Author(s):  
Halit Orhan ◽  
Dorina Raducanu
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Integral Transform ◽  
Starlike And Convex Functions ◽  
Complex Order

New subclasses of analytic functions are defined by using the function [Formula: see text] given by the integral transform [Formula: see text]. Bounds for the Fekete–Szegö coefficient functional [Formula: see text] for these classes of functions are derived.

scholarly journals Coefficient bounds for some families of starlike and convex functions of complex order

2007 ◽  
Vol 20 (12) ◽  
pp. 1218-1222 ◽  
Author(s):  
Osman Altıntaş ◽  
Hüseyin Irmak ◽  
Shigeyoshi Owa ◽  
H.M. Srivastava
Keyword(s):  
Convex Functions ◽  
Coefficient Bounds ◽  
Starlike And Convex Functions ◽  
Complex Order

scholarly journals Note on Neighborhoods of Some Classes of Analytic Functions with Negative Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Irina Dorca ◽  
Mugur Acu ◽  
Daniel Breaz
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike And Convex Functions ◽  
Inclusion Relations

In this paper, we prove several inclusion relations associated with the (n,δ) neighborhoods of some subclasses of starlike and convex functions with negative coefficients.

scholarly journals Convolution properties for subclasses of meromorphic univalent functions of complex order

Filomat ◽  
2012 ◽  
Vol 26 (1) ◽  
pp. 153-163 ◽  
Author(s):  
Teodor Bulboacă ◽  
Mohamed Aouf ◽  
Rabha El-Ashwah
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Complex Order ◽  
Inclusion Relations ◽  
Coefficient Inequalities ◽  
Convolution Properties ◽  
Meromorphic Univalent Functions

Using the new linear operator Lm(?,l)f(z) = 1/z + ??k=1(l/l+ ?k)m akzk-1, f ? ?, where l > 0, ? ? 0, and m ? N0 = N ? {0}, we introduce two subclasses of meromorphic analytic functions, and we investigate several convolution properties, coefficient inequalities, and inclusion relations for these classes.

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