Second Hankel Determinant for a Certain Subclass of Bi-univalent Functions

Mustafa, Nizami; Mrugusundaramoorthy, Gangadharan; Janani, T.

doi:10.1007/s00009-018-1165-1

Cited by 14 publications

(7 citation statements)

References 16 publications

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“…Until now, there are several results related to this problem (see, e.g. [1,2,4,7,10,12,13,17,20,23]).…”

Section: Definition 11 (Xu-xiao-srivastava [28]mentioning

confidence: 99%

Bounds of coefficients for classes of analytic functions related to hypergeometric functions

Xiong

2019

Filomat

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The main purpose of the present paper is to give some sharp coefficients bounds for a certain class of univalent analytic functions in unit open disk, which was defined by using principle of differential subordination and generalized hypergeometric function. As applications, we investigate the almost starlike-type functions, parabolic starlike-type functions and uniformly convex-type functions with conic domain. Our results extend some earlier works related to Ma-Minda starlike and convex functions.

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“…Until now, there are several results related to this problem (see, e.g. [1,2,4,7,10,12,13,17,20,23]).…”

Section: Definition 11 (Xu-xiao-srivastava [28]mentioning

confidence: 99%

Bounds of coefficients for classes of analytic functions related to hypergeometric functions

Xiong

2019

Filomat

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“…There are many findings related to the results of 𝐻 2 (1), 𝐻 2 (2) and 𝐻 2 (3) for subclasses of univalent and bi-univalent functions have been widely explored by mathematicians, among them are as [5,8,10,13,17,18,20,23].…”

Section: Introductionmentioning

confidence: 99%

Second Hankel Determinant of Bi-univalent Functions

Huey

Janteng

et al. 2023

Mal. J. Fund. Appl. Sci.

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Let be the class of functions which are analytic in the open unit disk and having the form . Denote to be the class for all functions in that are univalent in . Then, let denote the class of bi-univalent functions in . In this paper, we obtain the second Hankel determinant for certain classes of analytic bi-univalent function which are defined by subordinations in the open unit disk . In particular, we determine the initial coefficients and and obtained the upper bound for the functional of functions in the classes of analytic bi-univalent function which are defined by subordinations in .

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“…3 for the classes S * Σ (α) and C Σ (α) were obtained by Deniz et al [4] . Very soon, Orhan et al [19] reviewed the study of bound for the second Hankel determinant of the subclass M α Σ (β) of bi-univalent functions and Mustafa et al [16] improved the results obtained in [4]. Definition 1.1 [20] Let f ∈ A be normalized by f (0) = f ′ (0) − 1 = 0 in the unit disc U .…”

Section: Introductionmentioning

confidence: 99%