1. General coefficient estimates for bi-univalent functions: a new approach.
- Author
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AL-REFAI, Oqlah and ALI, Mohammed
- Subjects
- *
UNIVALENT functions , *STAR-like functions , *ESTIMATES , *CONVEX functions - Abstract
We prove for univalent functions f(z) = z + Σ∞k=n akzk; (n ≥ 2) in the unit disk U = {z : |z| < 1}) with f-1(w) = w + Σ∞ k=n bkwk; (|w| < r0(f), r0(f) ≥ 1 4) that b2n-1 = na²n - a2n-1 and bk = -ak for (n ≤ k ≤ 2n - 2). As applications, we find estimates for |an| whenever f is bi-univalent, bi-close-to-convex, bi-starlike, bi-convex, or for bi-univalent functions having positive real part derivatives in U. Moreover, we estimate |na2 n - a2n-1| whenever f is univalent in U or belongs to certain subclasses of univalent functions. The estimation method can be applied for various subclasses of bi-univalent functions in U and it helps to improve well-known estimates and to generalize some known results as shown in the last section. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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