A comprehensive subclass of bi-univalent functions associated with Chebyshev polynomials of the second kind

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.

Initial Coefficients Estimates and Fekete–Szegö Inequality Problem for a General Subclass of Bi-Univalent Functions Defined by Subordination

“…The set of Gegenbauer polynomials is a general subclass of Jacobi polynomials. For fundamental definitions and some important properties, the readers are referred to [16][17][18][19], and for neoteric investigations that connect geometric function theory with the classical orthogonal polynomials, see [20][21][22][23][24][25][26][27][28][29].…”

Exploiting the Pascal Distribution Series and Gegenbauer Polynomials to Construct and Study a New Subclass of Analytic Bi-Univalent Functions

“…To study the basic definitions and the most important properties of the classical orthogonal polynomials, we refer the reader to [3][4][5][6][7]. For a recent connection between the classical orthogonal polynomials and geometric function theory, we mention [8][9][10][11][12].…”

Necessary and Sufficient Conditions for Normalized Wright Functions to Be in Certain Classes of Analytic Functions

“…Special functions have been used extensively in many practical applications in physics, mathematics, and engineering. Recently, special functions have found many connections with geometric function theory, see [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. In this work, we consider the Wright function, which is a well-known special function defined as…”