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In the present paper, a new subclass of analytic and bi-univalent functions by means of Chebyshev polynomials is introduced. Certain coefficient bounds for functions belong to this subclass are obtained. Furthermore, the Fekete-Szegö problem in this subclass is solved.2010 Mathematics Subject Classification. Primary 30C45; Secondary 30C50.

This paper introduces a new class T γ α,β,k (η) of analytic functions which is defined by means of a linear operator involving generalized Mittag-Leffler function H γ α,β,k (f ). The results investigated in this paper include, an inclusion relation for functions in the class T γ α,β,k (η) and also some subordination results of the linear operator H γ α,β,k (f ). Several consequences of our results are also pointed out. Mathematics Subject Classification (2010): 33E12, 30C45.

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