scholarly journals p -Valent strongly starlike and strongly convex functions connected with linear differential Borel operator

2021 ◽  
Vol 26 (02) ◽  
pp. 137-148
Author(s):  
S. M. El-Deeb ◽  
G. Murugusundaramoorthy ◽  
A. Alburaikan
Keyword(s):  
Convex Functions ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Strongly Starlike ◽  
Linear Differential

scholarly journals The Fekete–Szegö problem for a class of analytic functions defined by Carlson–Shaffer operator

2014 ◽  
Vol 68 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Om P. Ahuja ◽  
Halit Orhan
Keyword(s):  
Differential Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Linear Differential Operator ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Strongly Starlike ◽  
Linear Differential

AbstractIn the present investigation we solve Fekete-Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions

scholarly journals On the order of strong starlikeness and the radii of starlikeness for of some close-to-convex functions

2019 ◽  
Vol 9 (4) ◽  
pp. 2367-2378 ◽  
Author(s):  
Mamoru Nunokawa ◽  
Janusz Sokół
Keyword(s):  
Convex Functions ◽  
Sufficient Conditions ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Japan Acad ◽  
Strongly Starlike ◽  
Small Improvement

Abstract In this paper we show several sufficient conditions for close-to-convex functions to be strongly starlike of some order. The results continue the line of study from the first author’s paper on the order of strong starlikeness of strongly convex functions, (Nunokawa in Proc Japan Acad Ser A 69(7):234–237, 1993). Also it appears an small improvement of a certain classical results of Ch. Pommerenke. As an application, we also derive estimates for the radii of star-likeness for close-to-convex functions.

scholarly journals ON THE NEIGHBOURHOODS OF STRONGLY CONVEX FUNCTIONS

1996 ◽  
Vol 27 (2) ◽  
pp. 103-109
Author(s):  
R. PARVATHAM ◽  
MILLICENT PREMABAI
Keyword(s):  
Convex Functions ◽  
Starlike Function ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Strongly Starlike Function ◽  
Strongly Starlike

In this paper neighbourhoods of strongly convex and strongly starlike function are determined.

scholarly journals Certain integral operator and strongly starlike functions

2002 ◽  
Vol 30 (9) ◽  
pp. 569-574 ◽  
Author(s):  
Jin-Lin Liu
Keyword(s):  
Integral Operator ◽  
Convex Functions ◽  
Starlike Functions ◽  
Strongly Convex Functions ◽  
Strongly Convex ◽  
Strongly Starlike Functions ◽  
Strongly Starlike

LetS∗(ρ,γ)denote the class of strongly starlike functions of orderρand typeγand letC(ρ,γ)be the class of strongly convex functions of orderρand typeγ. By making use of an integral operator defined by Jung et al. (1993), we introduce two novel families of strongly starlike functionsSβα(ρ,γ)andCβα(ρ,γ). Some properties of these classes are 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.

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