Fekete-Szegö Inequality for Analytic and Biunivalent Functions Subordinate to Gegenbauer Polynomials

Abstract

In the present paper, a subclass of analytic and biunivalent functions by means of Gegenbauer polynomials is introduced. Certain coefficients bound for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szegö problem for this subclass is solved. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

Applications of (M,N)-Lucas Polynomials on a Certain Family of Bi-Univalent Functions

“…Its origin is in the disproof by Fekete and Szegö in [1] of the Littlewood-Paley conjecture that the coefficients of odd univalent functions are bounded by unity. The Fekete-Szegö problem has been studied in recent years for many classes of univalent functions, see, for example: [2][3][4][5][6][8][9][10][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

On a subclass of bi-close-to-convex functions by means of the Gegenbauer polynomial

“…Here, S R indicates the class of univalent functions with real coefficients and coS R indicates the closed convex hull of S R . Recently, many researchers have discussed these polynomials for a subfamily of bi-univalent functions (see [7,8,19]).…”

A Comprehensive Family of Biunivalent Functions Defined byk-Fibonacci Numbers

“…The recent research trends are the outcomes of the study of functions in Σ based on any one of the above-mentioned polynomials, which can be seen in the recent papers [21][22][23][24][25][26][27][28]. Generally, interest was shown to estimate the first two coefficient bounds and the functional of Fekete-Szegö for some subfamilies of Σ.…”