Bounds on initial coefficients for a new subclass of bi-univ

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Lemma 1. Lemma 1.If p(z) ∈P, then |pn| ≤2 for each n ∈N where P be the class of functions analytic in U with ℜ(p(z)) > 0 and p(z) have the form p(z)…

Lemma 1.If p(z) ∈P, then |pn| ≤2 for each n ∈N where P be the class of functions analytic in U with ℜ(p(z)) > 0 and p(z) have the form p(z) = 1 + p1z+ p2z2 + p3z3 + ··· for z ∈U. 2 Main result Deﬁnition 1.A function f(z) ∈Σ given by (1) is said to be in the class TΣ[φ] if the following conditions are satisﬁed:

Theorem 1. Theorem 1.Let the function f(z) ∈Σ given by (1) be in the class TΣ[φ]. Then, |a2| ≤min 1,√B1

Theorem 1.Let the function f(z) ∈Σ given by (1) be in the class TΣ[φ]. Then, |a2| ≤min 1,√B1

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Bounds on initial coefficients for a new subclass of bi-univalent functions

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Results & Lemmas (2)

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