Subordination and superordination results associated with the generalized hypergeometric function

2014 ◽  
Vol 64 (5) ◽  
Author(s):  
Nanjundan Magesh ◽  
Jagadeesan Jothibasu ◽  
Sami Murthy
Keyword(s):  
Hypergeometric Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Generalized Hypergeometric Function ◽  
Hadamard Products

AbstractIn the present investigation, we obtain some subordination and superordination results involving Hadamard products for certain normalized analytic functions in the open unit disk. Relevant connections of the results, which are presented in this paper, with various other known results are also pointed out.

scholarly journals A Class of Integral Operators Preserving Subordination and Superordination for Analytic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
H. A. Al-Kharsani ◽  
N. M. Al-Areefi ◽  
Janusz Sokół
Keyword(s):  
Hypergeometric Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Type Theorem ◽  
Integral Operators ◽  
Gauss Hypergeometric Function ◽  
Open Unit ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Sandwich Type

The purpose of the paper is to investigate several subordination- and superordination-preserving properties of a class of integral operators, which are defined on the space of analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also presented. Moreover, we consider an application of the subordination and superordination theorem to the Gauss hypergeometric function.

scholarly journals On a geometric study of a class of normalized functions defined by Bernoulli’s formula

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Ibtisam Aldawish ◽  
Dumitru Baleanu
Keyword(s):  
Hypergeometric Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties ◽  
Central Purpose ◽  
Geometric Study

AbstractThe central purpose of this effort is to investigate analytic and geometric properties of a class of normalized analytic functions in the open unit disk involving Bernoulli’s formula. As a consequence, some solutions are indicated by the well-known hypergeometric function. The class of starlike functions is investigated containing the suggested class.

scholarly journals Partial sums of certain analytic functions

2001 ◽  
Vol 25 (12) ◽  
pp. 771-775 ◽  
Author(s):  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Partial Sums ◽  
Open Unit ◽  
Open Unit Disk

The object of the present paper is to consider the starlikeness and convexity of partial sums of certain analytic functions in the open unit disk.

scholarly journals The order of convexity for an integral operator

2016 ◽  
Vol 32 (1) ◽  
pp. 123-129
Author(s):  
VIRGIL PESCAR ◽  
◽  
CONSTANTIN LUCIAN ALDEA ◽  
◽  
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Order Of Convexity

In this paper we consider an integral operator for analytic functions in the open unit disk and we derive the order of convexity for this integral operator, on certain classes of univalent functions.

scholarly journals Strong Differential Subordination Results for Multivalent Analytic Functions Associated with Dziok-Srivastava Operator

2019 ◽  
pp. 159-168
Author(s):  
Abbas Kareem Wanas ◽  
Hala Abbas Mehdi
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Closed Unit Disk ◽  
Strong Differential Subordination

In this paper, by making use of the principle of strong subordination, we establish some interesting properties of multivalent analytic functions defined in the open unit disk and closed unit disk of the complex plane associated with Dziok-Srivastava operator.

scholarly journals On Certain Classes of Convex Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Young Jae Sim ◽  
Oh Sang Kwon
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Real Numbers ◽  
Inverse Functions

For real numbersαandβsuch that0≤α<1<β, we denote by𝒦α,βthe class of normalized analytic functions which satisfy the following two sided-inequality:α<ℜ1+zf′′z/f′z<β  z∈𝕌,where𝕌denotes the open unit disk. We find some relationships involving functions in the class𝒦(α,β). And we estimate the bounds of coefficients and solve the Fekete-Szegö problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or biunivalent functions.

scholarly journals Kudriasov Type Univalence Criteria for Some Integral Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Virgil Pescar ◽  
Nicoleta Breaz
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Univalence Criteria

We consider some integral operators defined by analytic functions in the open unit disk and derive new univalence criteria for these operators, using Kudriasov condition for a function to be univalent.

scholarly journals Starlikeness of Functions Defined by Third-Order Differential Inequalities and Integral Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
R. Chandrashekar ◽  
Rosihan M. Ali ◽  
K. G. Subramanian ◽  
A. Swaminathan
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Differential Inequalities ◽  
Third Order ◽  
Positive Order

Sufficient conditions are obtained to ensure starlikeness of positive order for analytic functions defined in the open unit disk satisfying certain third-order differential inequalities. As a consequence, conditions for starlikeness of functions defined by integral operators are obtained. Connections are also made to earlier known results.

Properties of the Salagean Operator

1998 ◽  
Vol 5 (4) ◽  
pp. 361-366
Author(s):  
Li Jian Lin ◽  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sălăgean Operator ◽  
Salagean Operator

Abstract The object of the present paper is to show the properties of the Salagean operator for analytic functions in the open unit disk. The main results obtained here extend and improve the earlier results obtained by several authors.

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

Mathematics ◽  
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.

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