No abstract

Our objective in this paper is to introduce and investigate a newly-constructed subclass of normalized analytic and bi-univalent functions by means of the Chebyshev polynomials of the second kind. Upper bounds for the second and third Taylor-Maclaurin coefficients, and also Fekete-Szegö inequalities of functions belonging to this subclass are founded. Several connections to some of the earlier known results are also pointed out.

The present paper introduces a new class of bi-univalent functions defined on a symmetric domain using Gegenbauer polynomials. For functions in this class, we have derived the estimates of the Taylor–Maclaurin coefficients, a2 and a3, and the Fekete-Szegö functional. Several new results follow upon specializing the parameters involved in our main results.

In the present paper, we define a new general subclass of bi-univalent functions involving a differential operator in the open unit disk U. For this purpose, we use the Faber polynomial expansions. Several connections to some of the earlier known results are also pointed out.The Koebe one-quarter theorem (for details, (see [10]), we know that the image of U under every function f ∈ A contains a disk of radius 1 4 . According to this, every function f ∈ A has an inverse map f −1 that satisfies the following conditions:and 2010 Mathematics Subject Classification. 30C45.