scholarly journals Some Classes of Co-Schwarzian Functions and Its Coefficient Inequality that Is Sharp

2021 ◽  
Vol 2 (4) ◽  
pp. 1-12
Author(s):  
Misha Rani ◽  
Gurmeet Singh
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Coefficient Inequality

In our present work, we defined an inequality called Fekete – Szegö Inequality for functions f(z) in the classes of starlike functions and convex functions along with subclasses of these classes.

scholarly journals ON SUBCLASSES OF UNIFORMLY CONVEX FUNCTIONS AND CORRESPONDING CLASS OF STARLIKE FUNCTIONS

1997 ◽  
Vol 28 (1) ◽  
pp. 17-32
Author(s):  
R. BHARATI ◽  
R. PARVATHAM ◽  
A. SWAMINATHAN
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Sufficient Condition ◽  
Uniformly Convex ◽  
Uniformly Convex Functions

We determine a sufficient condition for a function $f(z)$ to be uniformly convex of order et that is also necessary when $f(z)$ has negative coefficients. This enables us to express these classes of functions in terms of convex functions of particular order. Similar results for corresponding classes of starlike functions are also obtained. The convolution condition for the above two classes are discussed.

COEFFICIENT ESTIMATES FOR SOME CLASSES OF FUNCTIONS ASSOCIATED WITH -FUNCTION THEORY

2017 ◽  
Vol 95 (3) ◽  
pp. 446-456 ◽  
Author(s):  
SARITA AGRAWAL
Keyword(s):  
Convex Functions ◽  
Representation Theorem ◽  
Function Theory ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Coefficient Estimates

For every $q\in (0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach problem for the class of $q$-convex functions of order $\unicode[STIX]{x1D6FC}$ with $0\leq \unicode[STIX]{x1D6FC}<1$. In addition, we consider the Fekete–Szegö problem and the Hankel determinant problem for the class of $q$-starlike functions, leading to two conjectures for the class of $q$-starlike functions of order $\unicode[STIX]{x1D6FC}$ with $0\leq \unicode[STIX]{x1D6FC}<1$.

scholarly journals On convex functions of orderαand typeβ

1988 ◽  
Vol 11 (3) ◽  
pp. 485-492
Author(s):  
Wancang Ma
Keyword(s):  
Convex Functions ◽  
Starlike Functions

Owa [1] gave three subordination theorems for convex functions of orderαand starlike functions of orderα. Unfortunately, none of the theorems is correct. In this paper, similar problems are discussed for a generalized class and sharp results are given.

scholarly journals On a subclass ofn-starlike functions

2005 ◽  
Vol 2005 (17) ◽  
pp. 2841-2846 ◽  
Author(s):  
Mugur Acu ◽  
Shigeyoshi Owa
Keyword(s):  
Fixed Point ◽  
Convex Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Starlike And Convex Functions

In 1999, Kanas and Rønning introduced the classes of starlike and convex functions, which are normalized withf(w)=f'(w)−1=0andwa fixed point inU. In 2005, the authors introduced the classes of functions close to convex andα-convex, which are normalized in the same way. All these definitions are somewhat similar to the ones for the uniform-type functions and it is easy to see that forw=0, the well-known classes of starlike, convex, close-to-convex, andα-convex functions are obtained. In this paper, we continue the investigation of the univalent functions normalized withf(w)=f'(w)−1=0andw, wherewis a fixed point inU.

scholarly journals Integral operators of certain univalent functions

1985 ◽  
Vol 8 (4) ◽  
pp. 653-662 ◽  
Author(s):  
O. P. Ahuja
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Univalent Functions ◽  
Integral Operators ◽  
Starlike Functions ◽  
The Family

A functionf, analytic in the unit discΔ, is said to be in the familyRn(α)ifRe{(znf(z))(n+1)/(zn−1f(z))(n)}>(n+α)/(n+1)for someα(0≤α<1)and for allzinΔ, wheren ϵ No,No={0,1,2,…}. The The classRn(α)contains the starlike functions of orderαforn≥0and the convex functions of orderαforn≥1. We study a class of integral operators defined onRn(α). Finally an argument theorem is proved.

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 inequalities for univalent starlike functions

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Milutin Obradović ◽  
Saminathan Ponnusamy
Keyword(s):  
Unit Disk ◽  
Complex Number ◽  
Convex Functions ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Right Hand ◽  
Coefficient Inequalities ◽  
The Right ◽  
Necessary And Sufficient

AbstractLet A be the class of analytic functions in the unit disk $$\mathbb{D}$$ with the normalization f(0) = f′(0) − 1 = 0. In this paper the authors discuss necessary and sufficient coefficient conditions for f ∈ A of the form $$\left( {\frac{z} {{f(z)}}} \right)^\mu = 1 + b_1 z + b_2 z^2 + \ldots$$ to be starlike in $$\mathbb{D}$$ and more generally, starlike of some order β, 0 ≤ β < 1. Here µ is a suitable complex number so that the right hand side expression is analytic in $$\mathbb{D}$$ and the power is chosen to be the principal power. A similar problem for the class of convex functions of order β is open.

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.

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