Univalent Functions by Means of Chebyshev Polynomials

Abstract

The primary motivation of the paper is to define a new class $C{h}_{\delta }\left(\alpha ,\beta ,\gamma \right)$ which consists of univalent functions associated with Chebyshev polynomials. For this class, we determine the coefficient bound and convolution preserving property. Furthermore, by using subordination structure, two new subclasses of $C{h}_{\delta }\left(\alpha ,\beta ,\gamma \right)$ are introduced and denoted by $M\left({\lambda }_1,{\lambda }_2,s\right)$ and $N\left({\lambda }_1,{\lambda }_2,s\right)$ , respectively. For these subclasses, we obtain coefficient estimate, extreme points, integral representation, convexity, geometric interpretation, and inclusion results. Moreover, we prove that, under some restrictions on parameters, $C{h}_{\delta }\left(\alpha ,\beta ,\gamma \right)=N\left({\lambda }_1,{\lambda }_2,s\right)$ .