scholarly journals On analytic multivalent functions associated with lemniscate of Bernoulli

2020 ◽  
Vol 5 (3) ◽  
pp. 2261-2271
Author(s):  
Qaiser Khan ◽  
◽  
Muhammad Arif ◽  
Bakhtiar Ahmad ◽  
Huo Tang ◽  
...  
Keyword(s):  
Lemniscate Of Bernoulli

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.

The sharp bounds of the second and third Hankel determinants for the class 𝓢𝓛*

2020 ◽  
Vol 70 (4) ◽  
pp. 849-862
Author(s):  
Shagun Banga ◽  
S. Sivaprasad Kumar
Keyword(s):  
Triangle Inequality ◽  
Starlike Functions ◽  
Sharp Bound ◽  
The Novel ◽  
Sharp Bounds ◽  
Hankel Determinants ◽  
Lemniscate Of Bernoulli ◽  
Carathéodory Functions ◽  
The Right

AbstractIn this paper, we use the novel idea of incorporating the recently derived formula for the fourth coefficient of Carathéodory functions, in place of the routine triangle inequality to achieve the sharp bounds of the Hankel determinants H3(1) and H2(3) for the well known class 𝓢𝓛* of starlike functions associated with the right lemniscate of Bernoulli. Apart from that the sharp bound of the Zalcman functional: $\begin{array}{} |a_3^2-a_5| \end{array}$ for the class 𝓢𝓛* is also estimated. Further, a couple of interesting results of 𝓢𝓛* are also discussed.

scholarly journals Coefficient inequalities for a class of analytic functions associated with the lemniscate of Bernoulli

2018 ◽  
Vol 37 (4) ◽  
pp. 83-95
Author(s):  
Trailokya Panigrahi ◽  
Janusz Sokól
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Lemniscate Of Bernoulli ◽  
Toeplitz Determinant ◽  
Second Hankel Determinant ◽  
Coefficient Inequalities ◽  
The Right

In this paper, a new subclass of analytic functions ML_{\lambda}^{*}  associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}|  for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated.

89.23 The lemniscate of Bernoulli

2005 ◽  
Vol 89 (514) ◽  
pp. 89-93
Author(s):  
H. Martyn Cundy
Keyword(s):  
Lemniscate Of Bernoulli

scholarly journals Radii of starlikeness associated with the lemniscate of Bernoulli and the left-half plane

2012 ◽  
Vol 218 (11) ◽  
pp. 6557-6565 ◽  
Author(s):  
Rosihan M. Ali ◽  
Naveen K. Jain ◽  
V. Ravichandran
Keyword(s):  
Half Plane ◽  
Left Half ◽  
Lemniscate Of Bernoulli ◽  
Left Half Plane

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.

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