Abstract
In this paper we extend the concept of bi-univalent to the class of meromorphic functions. We propose to investigate the coefficient estimates for two classes of meromorphic bi-univalent functions. Also, we find estimates on the coefficients |b0| and |b1| for functions in these new classes. Some interesting remarks and applications of the results presented here are also discussed.
Results & Lemmas (3)
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Lemma 1.3. · coeff
Lemma 1.3. (see [17]) If ϕ ∈P, then |ck| ≦2 for each k, where P is the family of all functions ϕ, analytic in U, for which ℜ ϕ(z) > 0 (z…
Lemma 1.3. (see [17]) If ϕ ∈P, then |ck| ≦2 for each k, where P is the family of all functions ϕ, analytic in U, for which ℜ{ϕ(z)} > 0 (z ∈U), where ϕ(z) = 1 + c1z + c2z2 + · · · (z ∈U). 2. Coefficient Bounds for the Function Classes Σ∗ M(α, µ, λ) and eΣ∗ M(α, µ, λ) We begin this section by finding the estimates on the coefficients |b0| and |b1| for func- tions in the class Σ∗ M(α, µ, λ).
Theorem 2.1.
Theorem 2.1. Let the function f(z) given by (1.3) be in the following class: Σ∗ M(α, µ, λ) (0 ≤α < 1; λ ≥1; µ ≥0; λ > µ).
Theorem 2.1. Let the function f(z) given by (1.3) be in the following class: Σ∗ M(α, µ, λ) (0 ≤α < 1; λ ≥1; µ ≥0; λ > µ).
Theorem 2.2.
Theorem 2.2. Let the function f(z) given by (1.1) be in the following class: eΣ∗ M(α, µ, λ) (0 < α ≤1; λ ≥1; µ ≥0; λ > µ). Then |b0| ≤ 2α λ…
Theorem 2.2. Let the function f(z) given by (1.1) be in the following class: eΣ∗ M(α, µ, λ) (0 < α ≤1; λ ≥1; µ ≥0; λ > µ). Then |b0| ≤ 2α λ −µ (2.14) and |b1| ≤2α2 s 1 (2λ −µ)2 + (1 −µ)2
Function classes studied:
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