The main result shows that a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighbourhood consisting entirely of univalent functions. For the particular choice of a linear function in the hypothesis of the main theorem, we obtain a corollary which is equivalent to the classical Noshiro–Warschawski–Wolff univalence criterion. We also pr...

This article discusses two new subclasses of the bi-univalent functions category ∑ in open unit disk . The primary goal is to obtain estimations coefficients and for that are within these subclasses.

In this work, we introduce and investigate two new subclasses of the bi-univalent functions in which both f and f−1 are m -fold symmetric analytic functions. For functions in each of the subclasses introduced in this paper, we obtain the coefficient bounds for |am+1| and |a2m+1| .

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 the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.