The object of the present paper is to introduce and investigate new subclasses of the function class Σ of bi-univalent functions defined in the open unit disk U, involving quasi subordination. The coefficients estimate |a2| and |a3| for functions in these new subclasses are also obtained. c ©2017 All rights reserved.

In the present investigation, we define a new subclass of meromorphic bi-univalent functions class Σ′ of complex order γ ∈ C\{0}, and obtain the estimates for the coefficients |b0| and |b1|. Further we pointed out several new or known consequences of our result.

Bounds for the second Hankel determinant of certain bi-univalent functions Halit ORHAN, Nanjundan MAGESH, Jagadeesan YAMINI Department of Mathematics Faculty of Science, Atatürk University 25240 Erzurum, Turkey. Post-Graduate and Research Department of Mathematics, Government Arts College for Men, Krishnagiri 635001, Tamilnadu, India. Department of Mathematics, Govt First Grade College Vijayana...

We introduce and investigate two new subclasses ℳ σ (α, λ) and ℳ σ (β, λ) of meromorphic bi-univalent functions defined on Δ = {z : z ∈ ℂ, 1 < |z | <∞}. For functions belonging to these classes, estimates on the initial coefficients are obtained.

We introduce and investigate an interesting subclass NP(λ,δ)(Σ) (n, β; h) of analytic and bi-univalent functions in the open unit disk U. For functions belonging to the class NP(λ,δ)(Σ) (n, β; h), we obtain estimates on the first two Taylor-Maclaurin coefficients |a₂| and |a₃|.

In this paper, we investigate the coefficient bound estimates, second Hankel determinant, and Fekete-Szegö inequality for analytic bi-univalent function class, which call Mocanu type bi-starlike functions, related to a shell-shaped region in open unit disk complex plane. Some interesting special cases of results are also discussed.

In this paper, we have introduced and investigated two new subclasses of the function class Δ of bi-univalent functions defined in the open unit disk, which are associated with the generalized Hypergeometric function. Furthermore, we find estimates on the Taylor-Maclaurin coefficient | a2 | and | a3 | for the functions belonging to these new classes.

In this present investigation, we consider the subclass of analytic and bi-univalent functions associated with salagean operator consisting of the function class Σ in the unit open disk, which satisfies the qusi-subordination conditions. Also we obtain the first two Taylor-Maclaurin coefficients for functions in this new subclass. Mathematics Subject Classification: 30C45, 30C50