Early coefficients of the inverse of a regular convex function

“…To prove our main results, we need some preliminary lemmas. The first one is known as Carathéodory's lemma (see [2, p. 41] for example) and the second one is due to Libera and Złotkiewicz [10].…”

Section: Resultsmentioning

confidence: 99%

Logarithmic Coefficients of Some Close-to-Convex Functions

Ali

Allu

2016

Bull. Aust. Math. Soc.

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Abstract. The logarithmic coefficients γ n of an analytic and univalent function f in the unit disk D = {z ∈ C : |z| < 1} with the normalization for functions in a subclass of close-to-convex functions (with argument 0) and claimed that the estimate is sharp by providing a form of a extremal function. In the present paper, we pointed out that such extremal functions do not exist and the estimate is not sharp by providing a much more improved bound for the whole class of close-to-convex functions (with argument 0). We also determine a sharp upper bound of |γ 3 | for close-to-convex functions (with argument 0) with respect to the Koebe function.

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“…In the present article, by following the techniques devised by Libera and Złotkiewicz [14,15], we solve the Fekete-Szegö problem and also determine the sharp upper bound to the second Hankel determinant for the class R λ (a, c, A, B). We also investigate several majorization properties for certain subclasses of analytic functions in the unit disk U.…”

Section: (0) and F (U) ⊂ G(u)mentioning

confidence: 99%

On certain subclasses of analytic functions associated with the Carlson–Shaffer operator

Patel¹,

Sahoo²

2014

Annales UMCS, Mathematica

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Abstract. The object of the present paper is to solve Fekete-Szegö problem and determine the sharp upper bound to the second Hankel determinant for a certain class R λ (a, c, A, B) of analytic functions in the unit disk. We also investigate several majorization properties for functions belonging to a subclass R λ (a, c, A, B) of R λ (a, c, A, B) and related function classes. Relevant connections of the main results obtained here with those given by earlier workers on the subject are pointed out.

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Early coefficients of the inverse of a regular convex function

Abstract: ABSTRACT. UBing known properties of functions of positive real part it is shown that the first seven coefficients of the inverse of a regular univalent function mapping the disk onto a convex region are bounded by 1.

Cited by 212 publications

References 4 publications

Third Hankel Determinants for Subclasses of Univalent Functions

Third Hankel Determinants for Subclasses of Univalent Functions

Logarithmic Coefficients of Some Close-to-Convex Functions

On certain subclasses of analytic functions associated with the Carlson–Shaffer operator

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