Certain subclasses of analytic and bi-univalent functions

By Hari M. Srivastava, A. K. Mishra, P. Gochhayat. Applied Mathematics Letters, 2010

839 citations recorded by the source corpus.

In the present paper, we introduce and investigate two interesting subclasses of normalized analytic and univalent functions in the open unit disk U≔{z:z∈Cand|z|<1}, whose inverse has univalently analytic continuation to U. Among other results, bounds for the Taylor–Maclaurin coefficients |a2| and |a3| are found in our investigation.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a8bb98df2be76a0434fecdac7e4a0ccc90ba0b9b

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In Applied Mathematics

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Citations in the corpus

Second Hankel determinant for certain subclasses ofbi-univalent functions (2017, background): “Definition 1 (see [30]) A function f(z) given by (1.”
Estimates of Initial Coefficients for Bi-Univalent Functions (2014, background): “In the papers [1–15], the authors present some estimates for a 2 and a 3 , whilef is taken from various subclasses of Σ.”
Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator (2018, methodology): “[46], we choose to recall the following examples of functions in the class Σ : z 1 − z , − log(1 − z), 1 2 log (1 + z 1 − z ) ,”
Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions (2016, methodology): “[11] 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 Ali et al.”
New subclasses of analytic and bi-univalent functions endowed with coefficient estimate problems (2018, methodology): “o −∞. Thus, clearly, the 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”
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]).”
Subclasses of bi-univalent functions related to shell-like curves connected with Fibonacci numbers (2018, background): “Several authors have introduced and investigated subclasses of bi-univalent functions and obtained bounds for the initial coefficients (see [1, 2, 8, 12, 13, 14]).”
Initial coefficient bounds for a general class of bi-univalent functions (2013, background): “[14], Frasin and Aouf [6] and others [1, 5, 7, 17, 18], we propose to investigate the coefficient estimates for a general class of analytic and bi-univalent functions.”
Coefficient bounds for certain subclasses of bi-univalent functions (2016, background): “Frasin and Aouf (2011) also discovered that for A = I, the class ~E (a, A) can be reduced to the class 1ft that introduced and studied by Srivastava et al. (2010) as defined in the previous section.”
Coefficient estimates for a general subclass of analytic and bi-univalent functions of the Ma–Minda type (2017, neutral): “[25], introduced and investigated a number”
Coefficient estimates for a subclass of analytic and bi-univalent functions (2015, background): “[16] has apparently revived the study of analytic and bi-univalent functions in recent years (see also [39,40]).”
Coefficient Estimates for Two New Subclasses of Biunivalent Functions with respect to Symmetric Points (2015, background): “Bounds for the initial coefficients of several classes of functions were also investigated in [6–15].”