Hankel determinants for starlike and convex functions associated with sigmoid functions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Amina Riaz ◽  
Mohsan Raza ◽  
Derek K. Thomas
Keyword(s):  
Convex Functions ◽  
Sharp Bounds ◽  
Hankel Determinants ◽  
Starlike And Convex Functions ◽  
Sigmoid Functions

Abstract This paper is concerned with Hankel determinants for starlike and convex functions related to modified sigmoid functions. Sharp bounds are given for second and third Hankel determinants.

scholarly journals Second Hankel Determinant of Logarithmic Coefficients of Convex and Starlike Functions of Order Alpha

2021 ◽  
Author(s):  
Bogumiła Kowalczyk ◽  
Adam Lecko
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Hankel Determinant ◽  
Sharp Bounds ◽  
Starlike And Convex Functions ◽  
Second Hankel Determinant ◽  
Logarithmic Coefficients ◽  
Convex And Starlike Functions

AbstractIn the present paper, we found sharp bounds of the second Hankel determinant of logarithmic coefficients of starlike and convex functions of order $$\alpha $$ α .

Certain results on starlike and convex functions

2020 ◽  
Vol 4 (2) ◽  
pp. 1-14
Author(s):  
Pardeep Kaur ◽  
◽  
Sukhwinder Singh Billing ◽  
Keyword(s):  
Convex Functions ◽  
Starlike And Convex Functions

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 The second Hankel determinant for strongly convex and Ozaki close-to-convex functions

2021 ◽  
Author(s):  
Young Jae Sim ◽  
Adam Lecko ◽  
Derek K. Thomas
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Univalent Functions ◽  
Inverse Function ◽  
Invariance Property ◽  
Hankel Determinant ◽  
Sharp Bounds ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Second Hankel Determinant

AbstractLet f be analytic in the unit disk $${\mathbb {D}}=\{z\in {\mathbb {C}}:|z|<1 \}$$ D = { z ∈ C : | z | < 1 } , and $${{\mathcal {S}}}$$ S be the subclass of normalized univalent functions given by $$f(z)=z+\sum _{n=2}^{\infty }a_n z^n$$ f ( z ) = z + ∑ n = 2 ∞ a n z n for $$z\in {\mathbb {D}}$$ z ∈ D . We give sharp bounds for the modulus of the second Hankel determinant $$ H_2(2)(f)=a_2a_4-a_3^2$$ H 2 ( 2 ) ( f ) = a 2 a 4 - a 3 2 for the subclass $$ {\mathcal F_{O}}(\lambda ,\beta )$$ F O ( λ , β ) of strongly Ozaki close-to-convex functions, where $$1/2\le \lambda \le 1$$ 1 / 2 ≤ λ ≤ 1 , and $$0<\beta \le 1$$ 0 < β ≤ 1 . Sharp bounds are also given for $$|H_2(2)(f^{-1})|$$ | H 2 ( 2 ) ( f - 1 ) | , where $$f^{-1}$$ f - 1 is the inverse function of f. The results settle an invariance property of $$|H_2(2)(f)|$$ | H 2 ( 2 ) ( f ) | and $$|H_2(2)(f^{-1})|$$ | H 2 ( 2 ) ( f - 1 ) | for strongly convex functions.

scholarly journals Coefficient bounds for some families of starlike and convex functions of complex order

2007 ◽  
Vol 20 (12) ◽  
pp. 1218-1222 ◽  
Author(s):  
Osman Altıntaş ◽  
Hüseyin Irmak ◽  
Shigeyoshi Owa ◽  
H.M. Srivastava
Keyword(s):  
Convex Functions ◽  
Coefficient Bounds ◽  
Starlike And Convex Functions ◽  
Complex Order

Closure properties of operators on the Ma–Minda type starlike and convex functions

2011 ◽  
Vol 218 (3) ◽  
pp. 667-672 ◽  
Author(s):  
Abeer O. Badghaish ◽  
Rosihan M. Ali ◽  
V. Ravichandran
Keyword(s):  
Convex Functions ◽  
Closure Properties ◽  
Starlike And Convex Functions

Majorization of starlike and convex functions of complex order involving linear operators

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
K. Thilagavathi
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Linear Operators ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractThe main object of this present paper is to investigate the problem of majorization of certain class of analytic functions of complex order defined by the Dziok-Raina linear operator. Moreover we point out some new or known consequences of our main result.

scholarly journals Fekete–Szegö problem for certain subclasses of analytic functions

2012 ◽  
Vol 45 (4) ◽  
Author(s):  
Halit Orhan ◽  
Erhan Deniz ◽  
Murat Çağlar
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractIn this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order

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