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 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 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 Certain Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
N. Magesh
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Hypergeometric Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Generalized Hypergeometric Functions ◽  
Uniformly Convex Functions

Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the classTSml(α,β,γ). In particular, we obtain integral means inequalities for the functionfthat belongs to the classTSml(α,β,γ)in the unit disc.

scholarly journals Coefficient Bounds for Some Families of Starlike and Convex Functions of Reciprocal Order

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Muhammad Arif ◽  
Maslina Darus ◽  
Mohsan Raza ◽  
Qaiser Khan
Keyword(s):  
Upper Bound ◽  
Convex Functions ◽  
Hankel Determinant ◽  
Coefficient Estimates ◽  
Coefficient Bounds ◽  
Starlike And Convex Functions

The aim of the present paper is to investigate coefficient estimates, Fekete-Szegő inequality, and upper bound of third Hankel determinant for some families of starlike and convex functions of reciprocal order.

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.

A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator

2019 ◽  
Vol 69 (4) ◽  
pp. 825-832 ◽  
Author(s):  
Shahid Khan ◽  
Saqib Hussain ◽  
Muhammad A. Zaighum ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Extreme Point ◽  
Convex Functions ◽  
Starlike Functions ◽  
Starlike Function ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions ◽  
New Class ◽  
Closure Theorems

Abstract Making use of Ruscheweyh q-differential operator, we define a new subclass of uniformly convex functions and corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain, coefficient estimates, closure theorems and extreme point for the functions belonging to this new class. The results are generalized to families with fixed finitely many coefficients.

scholarly journals Coefficient estimates for certain subclass of analytic functions defined by subordination

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3307-3318
Author(s):  
Nirupam Ghosh ◽  
A. Vasudevarao
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Open Problems ◽  
Coefficient Bounds ◽  
Starlike And Convex Functions

In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with some open problems proposed by Q.H. Xu et al.([20], [21]). An application of Jack lemma for certain subclass of starlike functions has been discussed.

scholarly journals Hankel Determinant of Second Order for Some Classes of Analytic Functions

2021 ◽  
Author(s):  
Milutin Obradović ◽  
Nikola Tuneski
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Upper Bounds ◽  
Second Order ◽  
Hankel Determinant

Let ƒ be analytic in the unit disk B and normalized so that ƒ (z) = z + a2z2 + a3z3 +܁܁܁. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order α, Ozaki close-to-convex functions and two other classes of analytic functions. Some of the estimates are sharp.

scholarly journals Bounds for the Second Hankel Determinant of Certain Univalent Functions

2019 ◽  
Vol 8 (10S) ◽  
pp. 262-266
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Starlike And Convex Functions ◽  
Second Hankel Determinant

We study the estimates for the Second Hankel determinant of analytic functions. Our class includes (j,k)-convex, (j,k)-starlike functions and Ma-Minda starlike and convex functions..

scholarly journals Second Hankel Determinant of Logarithmic Coefficients of Convex and Starlike Functions of Order Alpha

2021 ◽  
Author(s):  
Bogumiła Kowalczyk ◽  
Adam Lecko
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Sharp Bounds ◽  
Starlike And Convex Functions ◽  
Second Hankel Determinant ◽  
Logarithmic Coefficients ◽  
Convex And Starlike Functions

AbstractIn the present paper, we found sharp bounds of the second Hankel determinant of logarithmic coefficients of starlike and convex functions of order $$\alpha $$ α .

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