scholarly journals Starlikeness associated with lemniscate of Bernoulli

Filomat ◽  
2019 ◽  
Vol 33 (7) ◽  
pp. 1937-1955 ◽  
Author(s):  
Vibha Madaan ◽  
Ajay Kumar ◽  
V. Ravichandran
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Second Order ◽  
Lemniscate Of Bernoulli

For an analytic function f on the unit disk D = {z : |z|<1} satisfying f (0) = 0 = f'(0) - 1, we obtain sufficient conditions so that f satisfies |(z f'(z)/f(z))2 - 1|< 1. The technique of differential subordination of first and second order is used. The admissibility conditions for lemniscate of Bernoulli are derived and employed in order to prove the main results.

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.

Sufficient conditions for Carathéodory functions and applications to univalent functions

2019 ◽  
Vol 69 (5) ◽  
pp. 1065-1076
Author(s):  
Oh Sang Kwon ◽  
Young Jae Sim
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Geometric Properties ◽  
First Order ◽  
Carathéodory Functions ◽  
Carathéodory Function

Abstract In this paper, the authors derive several sufficient conditions for a function to be the Carathéodory function in the unit disk 𝔻: = {z ∈ ℂ: |z| < 1}. More precisely, for given β ∈ (–π/2, π/2), γ ∈ [0, cosβ) and δ ∈ (0, π/2], we find some sufficient conditions for an analytic function p such that p(0) = 1 to satisfy Re{e−iβ p(z)} > γ or | arg {p(z)–γ} | < δ for all z ∈ 𝔻 by using the first-order differential subordination. We then apply the results obtained here in order to find some conditions for univalent functions with geometric properties such as spirallikeness and strongly starlikeness.

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.

Properties of Certain Multivalent Analytic Functions Associated with the Lemniscate of Bernoulli

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 160
Author(s):  
Likai Liu ◽  
Jin-Lin Liu
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Lemniscate Of Bernoulli

Using differential subordination, we consider conditions of β so that some multivalent analytic functions are subordinate to (1+z)γ (0<γ≤1). Notably, these results are applied to derive sufficient conditions for f∈A to satisfy the condition zf′(z)f(z)2−1<1. Several previous results are extended.

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 Radius of Star-Likeness for Certain Subclasses of Analytic Functions

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2448
Author(s):  
Caihuan Zhang ◽  
Mirajul Haq ◽  
Nazar Khan ◽  
Muhammad Arif ◽  
Khurshid Ahmad ◽  
...  
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Inverse Function ◽  
Open Unit ◽  
Open Unit Disk ◽  
Sine Function ◽  
Exponential Functions ◽  
Lemniscate Of Bernoulli ◽  
Rotation Function

In this paper, we investigate a normalized analytic (symmetric under rotation) function, f, in an open unit disk that satisfies the condition ℜfzgz>0, for some analytic function, g, with ℜz+1−2nzgz>0,∀n∈N. We calculate the radius constants for different classes of analytic functions, including, for example, for the class of star-like functions connected with the exponential functions, i.e., the lemniscate of Bernoulli, the sine function, cardioid functions, the sine hyperbolic inverse function, the Nephroid function, cosine function and parabolic star-like functions. The results obtained are sharp.

scholarly journals Second-Order Linear Differential Equations with Solutions in Analytic Function Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Jianren Long ◽  
Yu Sun ◽  
Shimei Zhang ◽  
Guangming Hu
Keyword(s):  
Analytic Function ◽  
Reproducing Kernel ◽  
Bloch Space ◽  
Sufficient Conditions ◽  
Representation Formula ◽  
Second Order ◽  
Order Linear ◽  
Linear Differential ◽  
The One ◽  
Reproducing Kernel Formula

This research is concerned with second-order linear differential equation f′′+A(z)f=0, where A(z) is an analytic function in the unit disc. On the one hand, some sufficient conditions for the solutions to be in α-Bloch (little α-Bloch) space are found by using exponential type weighted Bergman reproducing kernel formula. On the other hand, we find also some sufficient conditions for the solutions to be in analytic Morrey (little analytic Morrey) space by using the representation formula.

scholarly journals Sufficient conditions for starlikeness associated with parabolic region

2002 ◽  
Vol 32 (5) ◽  
pp. 319-324
Author(s):  
V. Ravichandran ◽  
A. Gangadharan ◽  
T. N. Shanmugam
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Convex Functions ◽  
Sufficient Conditions ◽  
Uniformly Convex ◽  
Uniformly Convex Functions

An analytic functionf(z)=z+a n+1 z n+1+⋯, defined on the unit disk△={z:|z|<1}, is in the classS pifz f′(z)/f(z)is in the parabolic regionRew>|w−1|. This class is closely related to the class of uniformly convex functions. Sufficient conditions for function to be inS pare obtained. In particular, we find condition onλsuch that the functionf(z), satisfying(1−α)(f(z)/z) μ+αf′(z)(f(z)/z) μ−1≺1+λz, is inS p.

scholarly journals Differential subordination and convexity criteria of integral operators

2017 ◽  
Vol 15 (1) ◽  
pp. 1509-1516
Author(s):  
R. Chandrashekar ◽  
See Keong Lee ◽  
K.G. Subramanian
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Integral Operators ◽  
Differential Subordination ◽  
Second Order ◽  
Fundamental Result ◽  
Open Unit ◽  
Open Unit Disk

Abstract A significant connection between certain second-order differential subordination and subordination of f′(z) is obtained. This fundamental result is next applied to investigate the convexity of analytic functions defined in the open unit disk. As a consequence, criteria for convexity of functions defined by integral operators are determined. Connections are also made to earlier known results.

scholarly journals Some applications of second-order differential subordination for a class of analytic function defined by the lambda operator

2020 ◽  
Vol 4 (2) ◽  
pp. 170-177
Author(s):  
B. Venkateswarlu ◽  
◽  
P. Thirupathi Reddy ◽  
S. Sridevi, Sujatha ◽  
◽  
...  
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Second Order ◽  
New Class

In this paper, we introduce a new class of analytic functions by using the lambda operator and obtain some subordination results.

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