Coefficient estimates and integral mean estimates for certain classes of analytic functions

A typical quandary in geometric functions theory is to study a functional composed of amalgamations of the coefficients of the pristine function. Conventionally, there is a parameter over which the extremal value of the functional is needed. The present paper deals with consequential functional of this type. By making use of Hohlov operator, a new subclass [Formula: see text] of analytic functions defined in the open unit disk is introduced. For both real and complex parameter, the sharp bounds for the Fekete–Szegö problems are found. An attempt has also been taken to found the sharp upper bound to the second and third Hankel determinant for functions belonging to this class. All the extremal functions are express in term of Gauss hypergeometric function and convolution. Finally, the sufficient condition for functions to be in [Formula: see text] is derived. Relevant connections of the new results with well-known ones are pointed out.

Download Full-text

Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

Mathematics ◽

10.3390/math8081334 ◽

2020 ◽

Vol 8 (8) ◽

pp. 1334

Author(s):

Bilal Khan ◽

Hari M. Srivastava ◽

Nazar Khan ◽

Maslina Darus ◽

Muhammad Tahir ◽

...

Keyword(s):

Unit Disk ◽

Analytic Functions ◽

Second Order ◽

Open Unit ◽

Open Unit Disk ◽

Hankel Determinant ◽

Coefficient Estimates ◽

Principle Of Subordination

First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(h) of the class R(h) of analytic functions, which are associated with the leaf-like domain in the open unit disk U, is given. Then, the coefficient estimates, the Fekete–Szegö problem, and the second-order Hankel determinant H2(1) for functions belonging to this class Rq(h) are investigated. Furthermore, similar results are examined and presented for the functions zf(z) and f−1(z). For the validity of our results, relevant connections with those in earlier works are also pointed out.

Download Full-text

Coefficient Estimates of Some Classes of Analytic Functions

Canadian Mathematical Bulletin ◽

10.4153/cmb-1983-032-6 ◽

1983 ◽

Vol 26 (2) ◽

pp. 202-208

Author(s):

Nicolas Samaris

Keyword(s):

Analytic Functions ◽

Positive Real Part ◽

Coefficient Estimates ◽

Positive Real ◽

Real Functions ◽

Typically Real ◽

Typically Real Functions

AbstractWe are concerned with coefficient estimates, and other similar problems, of the typically real functions and of the functions with positive real part. Following the stream of ideas in [1], new results and generalizations of others given in [1], [2] and [3] are obtained.

Download Full-text

Class of Analytic Function Related with Uniformly Convex and Janowski’s Functions

Journal of Function Spaces ◽

10.1155/2018/4679857 ◽

2018 ◽

Vol 2018 ◽

pp. 1-6 ◽

Cited By ~ 2

Author(s):

Akhter Rasheed ◽

Saqib Hussain ◽

Muhammad Asad Zaighum ◽

Maslina Darus

Keyword(s):

Analytic Function ◽

Analytic Functions ◽

Unit Disc ◽

Extreme Points ◽

Distortion Theorem ◽

Open Unit ◽

Uniformly Convex ◽

Coefficient Estimates ◽

Open Unit Disc

In this paper, we introduce a new subclass of analytic functions in open unit disc. We obtain coefficient estimates, extreme points, and distortion theorem. We also derived the radii of close-to-convexity and starlikeness for this class.

Download Full-text

Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Mathematics ◽

10.3390/math8020172 ◽

2020 ◽

Vol 8 (2) ◽

pp. 172 ◽

Cited By ~ 1

Author(s):

Hari M. Srivastava ◽

Ahmad Motamednezhad ◽

Ebrahim Analouei Adegani

Keyword(s):

Fractional Derivative ◽

Analytic Functions ◽

Univalent Functions ◽

Upper Bounds ◽

Differential Subordination ◽

Open Unit ◽

Open Unit Disk ◽

Coefficient Estimates ◽

Derivative Operator ◽

Faber Polynomial

In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results.

Download Full-text

Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions

Nagoya Mathematical Journal ◽

10.1017/s0027763000000854 ◽

1987 ◽

Vol 106 ◽

pp. 1-28 ◽

Cited By ~ 48

Author(s):

H. M. Srivastava ◽

Shigeyoshi Owa

Keyword(s):

Fractional Calculus ◽

Analytic Functions ◽

Hypergeometric Functions ◽

Linear Operators ◽

Coefficient Estimates ◽

Hadamard Products ◽

Generalized Hypergeometric Functions ◽

Hypergeometric Type ◽

Distortion Theorems ◽

Characterization Theorems

By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disk are introduced and studied systematically. The various results presented here include, for example, a number of coefficient estimates and distortion theorems for functions belonging to these subclasses, some interesting relationships between these subclasses, and a wide variety of characterization theorems involving a certain functional, some general functions of hypergeometric type, and operators of fractional calculus. Some of the coefficient estimates obtained here are fruitfully applied in the investigation of certain subclasses of analytic functions with fixed finitely many coefficients.

Download Full-text

A New Class of Analytic Functions Defined by Using Salagean Operator

International Journal of Analysis ◽

10.1155/2013/153128 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

R. M. El-Ashwah ◽

M. K. Aouf ◽

A. A. M. Hassan ◽

A. H. Hassan

Keyword(s):

Analytic Functions ◽

Extreme Points ◽

Distortion Theorem ◽

Partial Sums ◽

Coefficient Estimates ◽

Integral Means ◽

New Class ◽

Sălăgean Operator ◽

Salagean Operator ◽

Fractional Calculus Operators

We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

Download Full-text

Estimates for coefficients of certain analytic functions

Filomat ◽

10.2298/fil1711539r ◽

2017 ◽

Vol 31 (11) ◽

pp. 3539-3552 ◽

Cited By ~ 1

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).

Download Full-text

COEFFICIENT ESTIMATES FOR CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS OF COMPLEX ORDER

Taiwanese Journal of Mathematics ◽

10.11650/twjm/1500406441 ◽

2011 ◽

Vol 15 (5) ◽

pp. 2377-2386 ◽

Cited By ~ 9

Author(s):

Qing-Hua Xu ◽

Ying-Chun Gui ◽

H. M. Srivastava

Keyword(s):

Analytic Functions ◽

Coefficient Estimates ◽

Complex Order

Download Full-text