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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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In the present paper, we introduce a new generalized differentialoperator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ defined on the openunit disc $U=\left\{ z\in%%TCIMACRO{\U{2102} }%%BeginExpansion\mathbb{C}:\left\vert z\right\vert <1\right\} $. A novel subclass $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ by means of the operator $A_{\mu,\lambda,\sigma}^{m}(\alpha,\beta)$ is also introduced. Coefficient estimates, growth and distortion theorems, closuretheorems, and class preserving integral operators for functions in the class $\Omega_{m}^{\ast}(\delta,\lambda,\alpha,\beta,b)$ are discussed. Furthermore, sufficient conditions for close-to-convexity, starlikeness, and convexity for functions in the class $\Om are obtained

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In this paper, we introduce a subclass N n p,µ (α, β, A, B) of p-valent non-Bazilevič functions of order α + iβ. Some subordination relations and the inequality properties of p−valent functions are discussed. The results presented here generalize and improve some known results.2000 Mathematics Subject Classification. 30C45.