Coefficient estimates for a subclass of analytic and bi-univalent functions

By Hari M. Srivastava, Deepak Bansal. 2015

151 citations recorded by the source corpus.

Abstract In the present investigation, we consider a new subclass Σ ( τ , γ , φ ) of the class Σ consisting of analytic and bi-univalent functions in the open unit disk U . For functions belonging to the class Σ ( τ , γ , φ ) introduced here, we obtain estimates on the first two Taylor–Maclaurin coefficients | a 2 | and | a 3 | . Several related classes of analytic and bi-univalent functions in U are also considered and connections to some of the earlier known results are pointed out.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ad8771d7b6e8bb411310709a228055e255aca0a8

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

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]).”
The Fekete-Szegö functional problems for some subclasses of m-fold symmetric bi-univalent functions (2016, background): “Many researchers (see [6, 12, 13, 14, 16, 17, 18, 20]) recently investigated several interesting subclasses of the class Σ and found non-sharp estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3| .”
Coefficient estimates for a general subclass of analytic and bi-univalent functions of the Ma–Minda type (2017, unknown): “Then the class S (τ, μ, λ, γ ;φ) reduces to the class (τ, μ, φ) investigated by Srivastava and Bansal [18] which is defined by requiring that f ∈ , 1 + 1 τ [ f ′(z) + μz f ′′(z) − 1] ≺ φ(z) (1.13) and 1 + 1 τ [ g′(w) + μwg′′(w) − 1] ≺ φ(w), (1.14) where the function g is given by (1.4).”