2020
DOI: 10.2478/gm-2020-0010
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Certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers

Abstract: This paper is concerned with certain subclasses of univalent and bi-univalent functions related to shell-like curves connected with Fibonacci numbers. We find estimates of the initial coefficients |a2| and |a3| for the functions in these classes. Also we investigate upper bounds for the Fekete-Szegö functional and second Hankel determinant for these classes.

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Cited by 3 publications
(5 citation statements)
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“…But, the well known Koebe function 2 is not a member of Σ. Lewin [9] was the first, who investigated the class Σ and proved that |a 2 | < 1.51. Subsequently, bounds for the initial coefficients of various sub-classes of bi-univalent functions were studied by various authors in [4,5,8,10,11] and more recently by Abirami et al [1], Sivapalan et al [18] and Singh et al [15]- [17].…”
Section: Some Examples Of the Functions In The Classmentioning
confidence: 99%
“…But, the well known Koebe function 2 is not a member of Σ. Lewin [9] was the first, who investigated the class Σ and proved that |a 2 | < 1.51. Subsequently, bounds for the initial coefficients of various sub-classes of bi-univalent functions were studied by various authors in [4,5,8,10,11] and more recently by Abirami et al [1], Sivapalan et al [18] and Singh et al [15]- [17].…”
Section: Some Examples Of the Functions In The Classmentioning
confidence: 99%
“…Recently, in their pioneering work on the subject of bi-univalent functions, Srivastava et al [23] actually revived the study of the coefficient problems involving bi-univalent functions. Various subclasses of the bi-univalent function class Σ were introduced and non-sharp estimates on the first two coefficients |a 2 | and |a 3 | in the Taylor-Maclaurin series expansion (1) were found in several recent investigations (see, for example, [1,2,3,4,5,7,11,12,13,14,15,18,19,21,22,24,25] and references therein). The afore-cited papers on the subject were actually motivated by the pioneering work of Srivastava et al [23].…”
Section: Introductionmentioning
confidence: 99%
“…(see [17]). For more details one could refer recent works in this line from [1,3,4,5,11,13,14,18,19] and references therein.…”
Section: Introductionmentioning
confidence: 99%
“…To learn more about Fibonacci numbers, we may refer to [22], [31], [19], [25], and [2]. In [22], the authors determined the initial Taylor-Maclaurin coefficients |a 2 | and |a 3 | involving λ-pseudo bi-starlike functions and Sakaguchi functions related to shell-like curves connected with Fibonacci numbers.…”
Section: Introductionmentioning
confidence: 99%
“…Other few papers that also introduced and investigated new subclasses with Sakaguchi functions related to Fibonacci numbers are [18], [24] and [35]. Defining new subclasses of analytic biunivalent functions and investigating certain geometric properties associated with the Fibonacci numbers are also among the studies that have received much attention from researchers (see [2], [25], [30], [14], [31], [20], [15]).…”
Section: Introductionmentioning
confidence: 99%