Hankel, Toeplitz, and Hermitian-Toeplitz Determinants for Certain Close-to-convex Functions

Let f be analytic in $$\mathbb {D}=\{z\in \mathbb {C}:|z|<1\}$$ D = { z ∈ C : | z | < 1 } , and be given by $$f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$$ f ( z ) = z + ∑ n = 2 ∞ a n z n . We give sharp bounds for the second Hankel determinant, some Toeplitz, and some Hermitian-Toeplitz determinants of functions in the class of Ozaki close-to-convex functions, together with a sharp bound for the Zalcman functional $$J_{2,3}(f).$$ J 2 , 3 ( f ) .

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

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

Coefficient Bounds of Kamali-Type Starlike Functions Related with a Limacon-Shaped Domain

In this article, we familiarize a subclass of Kamali-type starlike functions connected with limacon domain of bean shape. We examine certain initial coefficient bounds and Fekete-Szegö inequalities for the functions in this class. Analogous results have been acquired for the functions f − 1 and ξ / f ξ and also found the upper bound for the second Hankel determinant a 2 a 4 − a 3 2 .

SECOND HANKEL DETERMINANT OF LOGARITHMIC COEFFICIENTS OF CONVEX AND STARLIKE FUNCTIONS

We begin the study of Hankel matrices whose entries are logarithmic coefficients of univalent functions and give sharp bounds for the second Hankel determinant of logarithmic coefficients of convex and starlike functions.

Coefficient functionals and radius problems of certain starlike functions

Ma–Minda class (of starlike functions) consists of normalized analytic functions [Formula: see text] defined on the unit disk for which the image of the function [Formula: see text] is contained in some starlike region lying in the right-half plane. In this paper, we obtain the best possible bounds on some initial coefficients for the inverse functions of Ma–Minda starlike functions. Further, the bounds on the Fekete–Szegö functional and the second Hankel determinant are computed for such functions. In addition, some sharp radius estimates are also determined.

Second Hankel Determinant for a Certain Subclass of Bi-Close to Convex Functions Defined by Kaplan

In this paper, we consider the class of strongly bi-close-to-convex functions of order α and bi-close-to-convex functions of order β. We obtain an upper bound estimate for the second Hankel determinant for functions belonging to these classes. The results in this article improve some earlier result obtained for the class of bi-convex functions.

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

Let 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.