scholarly journals Some Sufficient Conditions for Analytic Functions to Belong to Space

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaoge Meng
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions

This paper gives some sufficient conditions for an analytic function to belong to the space consisting of all analytic functions on the unit disk such

scholarly journals On q-ANALOGUE of Differential Subordination Associated with Lemniscate of Bernoulli

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Mohsan Raza ◽  
Hira Naz ◽  
Sarfraz Nawaz Malik ◽  
Sahidul Islam
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Open Unit ◽  
Sufficient Condition ◽  
Open Unit Disk ◽  
Lemniscate Of Bernoulli

This article comprises the study of differential subordination with analogue of q -derivative. It includes the sufficient condition on γ for 1 + γ ∂ z q h z / h n z to be subordinated by 1 + A z / 1 + B z , − 1 ≤ B < A ≤ 1 , and implies that h z ≺ 1 + z , where h z is the analytic function in the open unit disk. Moreover, certain sufficient conditions for q -starlikeness of analytic functions related with lemniscate of Bernoulli are determined.

scholarly journals Sufficient Conditions for Janowski Starlikeness

2007 ◽  
Vol 2007 ◽  
pp. 1-7 ◽  
Author(s):  
Rosihan M. Ali ◽  
V. Ravichandran ◽  
N. Seenivasagan
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk

LetA,B,D,E∈[−1,1]and letp(z)be an analytic function defined on the open unit disk,p(0)=1. Conditions onA,B,D, andEare determined so that1+βzp'(z)being subordinated to(1+Dz)/(1+Ez)implies thatp(z)is subordinated to(1+Az)/(1+Bz). Similar results are obtained by considering the expressions1+β(zp'(z)/p(z))and1+β(zp'(z)/p2(z)). These results are then applied to obtain sufficient conditions for analytic functions to be Janowski starlike.

scholarly journals A Generalized Class of Functions Defined by the q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2361
Author(s):  
Loriana Andrei ◽  
Vasile-Aurel Caus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Difference Operator ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
New Class ◽  
The Relationship ◽  
Class Of Functions

The goal of the present investigation is to introduce a new class of analytic functions (Kt,q), defined in the open unit disk, by means of the q-difference operator, which may have symmetric or assymetric properties, and to establish the relationship between the new defined class and appropriate subordination. We derived relationships of this class and obtained sufficient conditions for an analytic function to be Kt,q. Finally, in the concluding section, we have taken the decision to restate the clearly-proved fact that any attempt to create the rather simple (p,q)-variations of the results, which we have provided in this paper, will be a rather inconsequential and trivial work, simply because the added parameter p is obviously redundant.

scholarly journals Sufficiency Criteria for q -Starlike Functions Associated with Cardioid

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Saira Zainab ◽  
Ayesha Shakeel ◽  
Muhammad Imran ◽  
Nazeer Muhammad ◽  
Hira Naz ◽  
...  
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Image Domain ◽  
Lemniscate Of Bernoulli ◽  
Differential Subordinations

This article deals with the q -differential subordinations for starlike functions associated with the lemniscate of Bernoulli and cardioid domain. The primary goal of this work is to find the conditions on γ for 1 + γ z ∂ q   h z / h n   z   ≺ 1 + z , where h z is analytic function and is subordinated by the function which is producing cardioid domain as its image domain while mapping the open unit disk. Along with this, certain sufficient conditions for q -starlikeness of analytic functions are determined.

scholarly journals QKtype spaces of analytic functions

2006 ◽  
Vol 4 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Hasi Wulan ◽  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Nondecreasing Function ◽  
Necessary And Sufficient Conditions ◽  
Type Space ◽  
Necessary And Sufficient ◽  
Spaces Of Analytic Functions

For a nondecreasing functionK:[0,8)?[0,8)and0<p<8,-2<q<8, we introduceQK(p,q), aQKtype space of functions analytic in the unit disk and study the characterizations ofQK(p,q). Necessary and sufficient conditions onKsuch thatQK(p,q)become some known spaces are given.

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.

scholarly journals Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 133
Author(s):  
Andriy Zagorodnyuk ◽  
Anna Hihliuk
Keyword(s):  
Banach Space ◽  
Analytic Function ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Main Question ◽  
Dimensional Banach Space ◽  
Infinite Dimensional ◽  
Infinite Dimensional Banach Space ◽  
Taylor Polynomials

In this paper we investigate analytic functions of unbounded type on a complex infinite dimensional Banach space X. The main question is: under which conditions is there an analytic function of unbounded type on X such that its Taylor polynomials are in prescribed subspaces of polynomials? We obtain some sufficient conditions for a function f to be of unbounded type and show that there are various subalgebras of polynomials that support analytic functions of unbounded type. In particular, some examples of symmetric analytic functions of unbounded type are constructed.

scholarly journals Some Connections between Class𝒰- andα-Convex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Edmond Aliaga ◽  
Nikola Tuneski
Keyword(s):  
Convex Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk

The class𝒰(λ,μ)of normalized analytic functions that satisfy|(z/f(z))1+μ·f′(z)−1|<λfor allzin the open unit disk is studied and sufficient conditions for anα-convex function to be in𝒰(λ,μ)are given.

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 On the second hankel determinant for the kth-root transform of analytic functions

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 227-245 ◽  
Author(s):  
Najla Alarifi ◽  
Rosihan Ali ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Second Hankel Determinant ◽  
The Given ◽  
Logarithmically Convex Functions

Let f be a normalized analytic function in the open unit disk of the complex plane satisfying zf'(z)/f(z) is subordinate to a given analytic function ?. A sharp bound is obtained for the second Hankel determinant of the kth-root transform z[f(zk)/zk]1/k. Best bounds for the Hankel determinant are also derived for the kth-root transform of several other classes, which include the class of ?-convex functions and ?-logarithmically convex functions. These bounds are expressed in terms of the coefficients of the given function ?, and thus connect with earlier known results for particular choices of ?.

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