scholarly journals Convolution properties of a class of bounded analytic functions

1992 ◽  
Vol 45 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Zou Zhongzhu ◽  
Shigeyoshi Owa
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Bounded Analytic Functions ◽  
Class A ◽  
Convolution Properties ◽  
Class Of Functions

Let A be the class of functions f(z) which are analytic in the unit disk U with f(0) = f′(0) - 1 = 0. A subclass S(λ, M) (λ > 0, M > 0) of A is introduced. The object of the present paper is to prove some interesting convolution properties of functions f(z) belonging to the class S(λ, M). Also a certain integral operator J for f(z) in the class A is considered.

scholarly journals Some properties of multivalent analytic functions associated with an integral operator

2013 ◽  
Vol 21 (1) ◽  
pp. 277-284
Author(s):  
Yi-Hui Xu ◽  
Cai-Mei Yan
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Class Of Functions

Abstract Let A(p) denote the class of functions of the form f(z) = zp Σ∞k=1+p akzk (p ∈ N = {1, 2, 3,...}) which are analytic in the open unit disk U = {z : z ∈ C and |z| < 1} By making use of the Noor integral operator, we obtain some interesting properties of multivalent analytic functions.

scholarly journals A Class of Analytic Functions with Missing Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Ding-Gong Yang ◽  
Jin-Lin Liu
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Sharp Bounds ◽  
Radius Of Convexity ◽  
Convolution Properties ◽  
Class Of Functions

Let and denote the class of functions of the form which are analytic in the open unit disk and satisfy the following subordination condition , for, for. We obtain sharp bounds on , and coefficient estimates for functions belonging to the class . Conditions for univalency and starlikeness, convolution properties, and the radius of convexity are also considered.

scholarly journals On the univalency for certain subclass of analytic functions involving Ruscheweyh derivatives

2002 ◽  
Vol 31 (9) ◽  
pp. 567-575 ◽  
Author(s):  
Liu Mingsheng
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Covering Theorem ◽  
Inclusion Relations ◽  
Special Case ◽  
Class Of Functions

LetHbe the class of functionsf(z)of the formf(z)=z+∑ K=2 + ∞a k z k, which are analytic in the unit diskU={z;|z|<1}. In this paper, we introduce a new subclassBλ(μ,α,ρ)ofHand study its inclusion relations, the condition of univalency, and covering theorem. The results obtained include the related results of some authors as their special case. We also get some new results.

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 Poisson distribution series on a general class of analytic functions

2020 ◽  
Vol 24 (2) ◽  
pp. 241-251
Author(s):  
Basem A. Frasin
Keyword(s):  
Integral Operator ◽  
Poisson Distribution ◽  
Analytic Functions ◽  
General Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Class A ◽  
Poisson Distribution Series ◽  
Necessary And Sufficient

The main object of this paper is to find necessary and sufficient conditions for the Poisson distribution series to be in a general class of analytic functions with negative coefficients. Further, we consider an integral operator related to the Poisson distribution series to be in this class. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

scholarly journals Subclasses of Analytic Functions Defined by Generalized Hypergeometric Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Badr S. Alkahtani ◽  
Saima Mustafa ◽  
Teodor Bulboacă
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Generalized Hypergeometric Functions ◽  
Radius Problems ◽  
Inclusion Results

We introduce a new subclass of analytic functions in the unit diskU, defined by using the generalized hypergeometric functions, which extends some previous well-known classes defined by different authors. Inclusion results, radius problems, and some connections with the Bernardi-Libera-Livingston integral operator are discussed.

scholarly journals Geometric Properties of a New Integral Operator

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Roberta Bucur ◽  
Loriana Andrei ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Geometric Properties ◽  
Special Cases

We obtain sufficient conditions for the univalence, starlikeness, and convexity of a new integral operator defined on the space of normalized analytic functions in the open unit disk. Some subordination results for the new integral operator are also given. Several corollaries follow as special cases.

scholarly journals Univalence conditions for a general integral operator

2015 ◽  
Vol 23 (1) ◽  
pp. 213-224
Author(s):  
Adriana Oprea ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
General Integral ◽  
General Integral Operator

AbstractFor analytic functions in the open unit disk U, we define a new general integral operator. The main object of the this paper is to study this new integral operator and to determine univalence conditions of it. Several corollaries of the main results are also considered.

scholarly journals Classes of an univalent integral operator

2021 ◽  
Vol 66 (2) ◽  
pp. 339-351
Author(s):  
Barbatu Camelia ◽  
Daniel Breaz
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
General Integral ◽  
General Integral Operator

"In this paper we introduce a new general integral operator for analytic functions in the open unit disk U and we obtain su cient conditions for univalence of this integral operator."

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