New subclasses of bi-univalent functions

By Basem Aref Frasin, Mohamed Kamal Aouf. Applied Mathematics Letters, 2011

520 citations recorded by the source corpus.

Abstract In this paper, we introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients | a 2 | and | a 3 | for functions in these new subclasses.

Subfields: Geometry and Topology, Polymers and Plastics

View Paper: https://www.semanticscholar.org/paper/e6c3342924f893965259ce5b495242360dc2f58a

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Citations in the corpus

Coefficient estimates for a general subclass of analytic and bi-univalent functions of the Ma–Minda type (2017, unknown): “[8] essentially revived the investigation of various subclasses of the bi-univalent function class Σ in recent years; it was followed by such works as those by Frasin and Aouf [4], Xu et al.”
Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions (2016, background): “[12], and Jahangiri and Hamidi [7](see also [1, 4, 6, 10], and the references cited in each of them).”
Faber polynomial coefficient bounds for a subclass of bi-univalent functions (2015, background): “Recently, many authors investigated bounds for various subclasses of bi-univalent functions ([5], [10], [13], [18], [19], [21], [24], [27], [28], [29]).”
Coefficient Bounds for a Certain Class of Analytic and Bi-Univalent Functions (2015, background): “In fact, judging by the remarkable flood of papers on the subject (see, for example, [5–7, 9–12, 15–17, 19–21, 23, 26, 27, 29, 30]), the recent pioneering work of Srivastava et al.”
Coefficient estimates for a subclass of analytic and bi-univalent functions (2015, result): “In fact, judging by the remarkable flood of papers on non-sharp estimates on the first two coefficients ja2j and ja3j of various subclasses of the bi-univalent function class R (see, for example, [19–30,35,31–34,15,36–38]), the above-cited recent pioneering work of Srivastava et al.”
Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator (2018, background): “[46], many authors investigated the coefficient bounds for various subclasses of bi-univalent functions (see, for example, [4], [15], [24], [40], [41], [42], [43], [44], [49] and [50]).”
Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions (2014, methodology): “(i) For μ = 1, we obtain the bi-univalent function class N 1 Σ(α,λ) = BΣ(α,λ) introduced by Frasin and Aouf [13].”
Coefficient bounds for certain subclasses of bi-univalent functions (2013, background): “Other common examples of functions in S such as z − z2 2 and z 1−z2 are also not members of Σ (see [5, 12]).”
Chebyshev polynomial coefficient estimates for a class of analytic bi-univalent functions related to pseudo-starlike functions (2017, background): “For a history and examples of functions which are (or which are not) in the class , together with various other properties of subclasses of bi-univalent functions one can refer [1,4,6,13,15,17,19,21].”
Faber Polynomial Coefficient Estimates for Bi-univalent Functions Defined by the Tremblay Fractional Derivative Operator (2018, background): “When γ = μ = 1, we can deduce the corresponding coefficient estimates for functions in the class B (β, λ) which was studied recently by Frasin and Aouf [9].”
Fekete-Szego Inequality for Analytic and Bi-univalent Functions Subordinate to Chebyshev Polynomials (2018, background): “[11] B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl.”
New subclasses of analytic and bi-univalent functions endowed with coefficient estimate problems (2018, methodology): “he image of the domain does not contain the unit disk U. For a brief history and some intriguing examples of functions and characterization of the class Σ, see Srivastava et al. [16], Frasin and Aouf [9], and Yousef et al. [20]. In 1967, Lewin [10] investigated the bi-univalent function class Σ and ”