Coefficient bounds for a certain class of close-to-convex functions

2018 ◽  
Author(s):  
Abdullah Yahya ◽  
Shaharuddin Cik Soh
Keyword(s):  
Convex Functions ◽  
Coefficient Bounds

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 Certain Subclasses of β-Uniformly q-Starlike and β-Uniformly q-Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Eman S. A. AbuJarad ◽  
Mohammed H. A. AbuJarad ◽  
Thabet Abdeljawad ◽  
Fahd Jarad
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Coefficient Bounds

In this paper, the authors introduced certain subclasses β-uniformly q-starlike and β-uniformly q-convex functions of order α involving the q-derivative operator defined in the open unit disc. Coefficient bounds were also investigated.

scholarly journals Subclasses of close-to-convex functions

1983 ◽  
Vol 6 (3) ◽  
pp. 449-458 ◽  
Author(s):  
E. M. Silvia
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Integral Operators ◽  
Coefficient Bounds ◽  
Class Of Functions

Let𝒦[C,D],−1≤D<C≤1, denote the class of functionsg(z),g(0)=g′(0)−1=0, analytic in the unit diskU={z:|z|<1}such that1+(zg″(z)/g′(z))is subordinate to(1+Cz)/(1+Dz),z ϵ U. We investigate the subclasses of close-to-convex functionsf(z),f(0)=f′(0)−1=0, for which there existsg ϵ 𝒦[C,D]such thatf′/g′is subordinate to(1+Az)/(1+Bz),−1≤B<A≤1. Distortion and rotation theorems and coefficient bounds are obtained. It is also shown that these classes are preserved under certain integral operators.

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).

Coefficient bounds for certain subclasses of close-to-convex functions of complex order

Filomat ◽  
2017 ◽  
Vol 31 (20) ◽  
pp. 6401-6408 ◽  
Author(s):  
Serap Bulut
Keyword(s):  
Differential Equation ◽  
Convex Functions ◽  
Coefficient Bounds ◽  
Complex Order ◽  
Type Differential Equation

In this paper, we determine the coefficient bounds for functions in certain subclasses of close-to-convex functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy-Euler-type differential equation of order m. Relevant connections of some of the results obtained with those in earlier works are also provided.

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.

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 Some classes of alpha-quasi-convex functions

1988 ◽  
Vol 11 (3) ◽  
pp. 497-501 ◽  
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Integral Representation ◽  
Unit Disk ◽  
Convex Functions ◽  
Integral Operators ◽  
Coefficient Bounds ◽  
Class Of Functions

LetC[C,D],−1≤D<C≤1denote the class of functionsg,g(0)=0,g′(0)=1, analytic in the unit diskEsuch that(zg′(z))′g′(z)is subordinate to1+CZ1+DZ,z∈E. We investigate some classes of Alpha-Quasi-Convex Functionsf, withf(0)=f′(0)−1=0for which there exists ag∈C[C,D]such that(1−α)f′(z)g′(z)+α(zf′(z))′g′(z)is subordinate to1+AZ1+BZ′,−1≤B<A≤1. Integral representation, coefficient bounds are obtained. It is shown that some of these classes are preserved under certain integral operators.

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.

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