Initial bounds for certain subclasses of generalized salagean type Bi-univalent functions associated with the Horadam polynomials

• Main Authors: Sakar, F. Muge, Aydogan, S. Melike
• Format: Article
• Language: English
• Published: Penerbit Universiti Kebangsaan Malaysia 2019
• Online Access: http://journalarticle.ukm.my/13867/1/jqma-15-1-paper8.pdf; http://journalarticle.ukm.my/13867/; http://www.ukm.my/jqma/jqma15_1a.html

This study proposes the use of Horadam polynomials which are known as their special cases, such as the Fibonacci polynomials, the Lucas polynomials, the Pell polynomials, the Pell-Lucas polynomials, and Chebyshev polynomials of the second kind. The aim of this study is to introduce a new subclass of generalized Sǎlǎgean type bi-univalent functions using Hadamard product and defined by Horadam polynomials ()nx in the open unit disk {z:1}.UCz We obtained coefficient estimates of the Taylor-Maclaurin 2a and 3a for functions f belonging to this newly defined subclass. Fekete-Szegö inequalities were also studied. Moreover, we give some interesting results using the relation between Sǎlǎgean’s differential operator and generalized Sǎlǎgean differential operator.