Coefficient estimates for some general subclasses of analytic and bi-univalent functions

Srivástava, H. M.; Gaboury, Sébastien; Ghanim, F.

doi:10.1007/s13370-016-0478-0

Cited by 99 publications

(51 citation statements)

References 11 publications

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“…The interested reader can find a brief historical overview of functions in the class Σ in the work of Srivastava et al [2], which actually revised the study of the bi-univalent function class Σ, as well as in the references cited therein. Bounds for the first two Taylor-Maclaurin coefficients |a 2 | and |a 3 | of various subclasses of bi-univalent functions were obtained in a number of sequels to [2] including (among others) [3][4][5][6][7][8][9][10][11][12]. As a matter of fact, considering the remarkably huge amount of papers on the subject, the pioneering work by Srivastava et al [2] appears to have successfully revived the study of analytic and bi-univalent functions in recent years.…”

Section: Introduction Definitions and Preliminariesmentioning

confidence: 99%

Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

2020

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In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results.

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Section: Introduction Definitions and Preliminariesmentioning

confidence: 99%

Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

2020

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“…Clearly, upon substituting from (21) and (22) into (16) and (17), respectively, if we make use of (11), we …nd that…”

Section: Coefficient Bounds For the Class B ('; ; )mentioning

confidence: 99%

Bounds for initial MacLaurin coefficients of a subclass of bi-univalent functions associated with subordination

Motamednezhad¹,

Nosrati²,

Zaker³

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…For a brief history of functions in the class Σ, see [24][25][26][27]. More recent studies inspired by Srivastava et al's [23] ground-breaking investigations in this area examine coefficient bounds in a range of bi-univalent function subclasses (as in e.g., [8,[28][29][30][31][32][33]).…”

Section: Introductionmentioning

confidence: 99%

Coefficient Estimates for a Subclass of Bi-Univalent Functions Defined by q-Derivative Operator

Elhaddad

Darus

2020

Mathematics

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Recently, a number of features and properties of interest for a range of bi-univalent and univalent analytic functions have been explored through systematic study, e.g., coefficient inequalities and coefficient bounds. This study examines S q δ ( ϑ , η , ρ , ν ; ψ ) as a novel general subclass of Σ which comprises normalized analytic functions, as well as bi-univalent functions within Δ as an open unit disk. The study locates estimates for the | a 2 | and | a 3 | Taylor–Maclaurin coefficients in functions of the class which is considered. Additionally, links with a number of previously established findings are presented.

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Coefficient estimates for some general subclasses of analytic and bi-univalent functions

Cited by 99 publications

References 11 publications

Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Bounds for initial MacLaurin coefficients of a subclass of bi-univalent functions associated with subordination

Coefficient Estimates for a Subclass of Bi-Univalent Functions Defined by q-Derivative Operator

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