scholarly journals Bounded Doubly Close-to-Convex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Dorina Răducanu
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Coefficient Bounds ◽  
New Class ◽  
Radius Of Convexity ◽  
Distortion Theorems

We consider a new classCC(α,β)of bounded doubly close-to-convex functions. Coefficient bounds, distortion theorems, and radius of convexity for the classCC(α,β)are investigated. A corresponding class of doubly close-to-starlike functionsS*S(α,β)is also considered.

ON SOME PROPERTIES OF A GENERALIZED CLASS OF CLOSE-TO-STARLIKE FUNCTIONS

2019 ◽  
Vol 4 (1) ◽  
pp. 193
Author(s):  
Ajab Bai Akbarally ◽  
Nor Siti Khadijah
Keyword(s):  
Univalent Functions ◽  
Starlike Functions ◽  
Starlike Function ◽  
Coefficient Bounds ◽  
New Class ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

In this paper, we consider a new class of close-to-starlike functions  defined by the Carlson-Shaffer operator. Let denote the class of analytic univalent functions defined by then  ifsatisfy the condition  ,where  and is a starlike function. Properties  of the class  such as the coefficient bounds, growth and distortion theorems and radius properties are investigated. 

scholarly journals Properties of Functions Formed Using the Sakaguchi and Gao-Zhou Concept

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 310
Author(s):  
Jonathan Aaron Azlan Mosiun ◽  
Suzeini Abdul Halim
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
New Class ◽  
Radius Of Convexity

This paper introduces a new class related to close-to-convex functions denoted by K s k , N . This class is based on combining the concepts of starlike functions with respect to N-ply symmetry points of the order α , introduced by Chand and Singh; and K s ( k ) , introduced by Wang, Gao, and Yuan, which are generalizations of the classes of functions introduced by Sakaguchi and Gao and Zhou, respectively. We investigate the class for several properties including coefficient estimates, distortion and growth theorems, and the radius of convexity.

scholarly journals Coefficient Estimates for a Subclass of Meromorphic Multivalent q-Close-to-Convex Functions

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1840
Author(s):  
Lei Shi ◽  
Bakhtiar Ahmad ◽  
Nazar Khan ◽  
Muhammad Ghaffar Khan ◽  
Serkan Araci ◽  
...  
Keyword(s):  
Differential Operator ◽  
Convex Functions ◽  
Starlike Functions ◽  
Distortion Theorem ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Growth Theorem ◽  
New Class ◽  
Radius Of Convexity

By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we investigate some useful properties such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity for this new subclass.

scholarly journals Estimates for coefficients of certain analytic functions

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3539-3552 ◽  
Author(s):  
V. Ravichandran ◽  
Shelly Verma
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Coefficient Problem ◽  
Inverse Coefficient Problem ◽  
Coefficient Bounds ◽  
Inverse Functions ◽  
Inverse Coefficient

For -1 ? B ? 1 and A > B, let S*[A,B] denote the class of generalized Janowski starlike functions consisting of all normalized analytic functions f defined by the subordination z f'(z)/f(z)< (1+Az)/(1+Bz) (?z?<1). For -1 ? B ? 1 < A, we investigate the inverse coefficient problem for functions in the class S*[A,B] and its meromorphic counter part. Also, for -1 ? B ? 1 < A, the sharp bounds for first five coefficients for inverse functions of generalized Janowski convex functions are determined. A simple and precise proof for inverse coefficient estimations for generalized Janowski convex functions is provided for the case A = 2?-1(?>1) and B = 1. As an application, for F:= f-1, A = 2?-1 (?>1) and B = 1, the sharp coefficient bounds of F/F' are obtained when f is a generalized Janowski starlike or generalized Janowski convex function. Further, we provide the sharp coefficient estimates for inverse functions of normalized analytic functions f satisfying f'(z)< (1+z)/(1+Bz) (?z? < 1, -1 ? B < 1).

scholarly journals On close-to-convex functions of complex order

1990 ◽  
Vol 13 (2) ◽  
pp. 321-330 ◽  
Author(s):  
H. S. Al-Amiri ◽  
Thotage S. Fernando
Keyword(s):  
Convex Functions ◽  
Nonnegative Integer ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Covering Theorems

The classS*(b)of starlike functions of complex orderbwas introduced and studied by M.K. Aouf and M.A. Nasr. The authors using the Ruscheweyh derivatives introduce the classK(b)of functions close-to-convex of complex orderb,b≠0and its generalization, the classesKn(b)wherenis a nonnegative integer. HereS*(b)⊂K(b)=K0(b). Sharp coefficient bounds are determined forKn(b)as well as several sufficient conditions for functions to belong toKn(b). The authors also obtain some distortion and covering theorems forKn(b)and determine the radius of the largest disk in which everyf∈Kn(b)belongs toKn(1). All results are sharp.

scholarly journals On a subclass of close-to-convex harmonic mappings

2020 ◽  
pp. 2150102
Author(s):  
Rajbala ◽  
Jugal K. Prajapat
Keyword(s):  
Unit Disk ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Basic Properties ◽  
New Class ◽  
Radius Of Convexity

In this paper, we introduce a new class of sense preserving harmonic mappings [Formula: see text] in the open unit disk and prove that functions in this class are close-to-convex. We give some basic properties such as coefficient bounds, growth estimates, convolution and determine the radius of convexity for the sections of functions belonging to this family. In addition, we construct certain harmonic univalent polynomials belonging to this family.

scholarly journals Certain New Classes of Analytic Functions with Varying Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
R. M. El-Ashwah ◽  
M. K. Aouf ◽  
A. A. M. Hassan ◽  
A. H. Hassan
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Uniformly Convex Functions ◽  
Distortion Theorems ◽  
Uniformly Starlike Functions ◽  
Uniformly Starlike ◽  
Varying Arguments

We introduce certain new classes κ−VST(α,β) and κ−VUCV(α,β), which represent the κ uniformly starlike functions of order α and type β with varying arguments and the κ uniformly convex functions of order α and type β with varying arguments, respectively. Moreover, we give coefficients estimates, distortion theorems, and extreme points of these classes.

scholarly journals Radius of Convexity of Sections of a Class of Close-to-Convex Functions of Order α

2018 ◽  
Vol 60 (1) ◽  
pp. 29-35
Author(s):  
B. Usna Banu ◽  
G. P. Youvaraj
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Coefficient Bounds ◽  
Radius Of Convexity

Abstract In this paper we study radius of convexity of sections of a class of univalent close-to-convex functions on 𝔻 = {z ∈ ℂ: |z| < 1}. For functions in this class, coefficient bounds, an integral representation and radius of convexity of nth sections have been obtained.

scholarly journals Applications of fractional calculus to $ k $-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $

2007 ◽  
Vol 38 (2) ◽  
pp. 103-109 ◽  
Author(s):  
Ajab Akbarally ◽  
Maslina Darus
Keyword(s):  
Fractional Calculus ◽  
Convex Functions ◽  
Analytic Functions ◽  
Uniformly Convex ◽  
Coefficient Bounds ◽  
Uniformly Convex Functions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems ◽  
Uniformly Starlike

A new subclass of analytic functions $ k-SP_\lambda(\alpha) $ is introduced by applying certain operators of fractional calculus to $k$-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $. Some theorems on coefficient bounds and growth and distortion theorems for this subclass are found. The radii of close to convexity, starlikeness and convexity for this subclass is also derived.

scholarly journals Radii of starlikeness and convexity for functions with fixed second coefficient defined by subordination

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 553-561 ◽  
Author(s):  
Rosihan Ali ◽  
Eun Cho ◽  
Kumar Jain ◽  
V. Ravichandran
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Radius Of Starlikeness ◽  
Uniformly Convex Functions ◽  
Lemniscate Of Bernoulli ◽  
Strongly Starlike Functions ◽  
Special Cases ◽  
Radius Of Convexity ◽  
Strongly Starlike

Several radii problems are considered for functions f (z) = z + a2z2 + ... with fixed second coefficient a2. For 0 ? ? < 1, sharp radius of starlikeness of order ? for several subclasses of functions are obtained. These include the class of parabolic starlike functions, the class of Janowski starlike functions, and the class of strongly starlike functions. Sharp radius of convexity of order ? for uniformly convex functions, and sharp radius of strong-starlikeness of order ? for starlike functions associated with the lemniscate of Bernoulli are also obtained as special cases.

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