Abstract
Some sharp estimates of coefficients, distortion, and growth for harmonic mappings with analytic parts convex or starlike functions of orderβare obtained. We also give area estimates and covering theorems. Our main results generalise those of Klimek and Michalski.
Highlights
Let S denote the class of functions of the form f(z) = z +
In [5], the classes of starlike and convex functions of order β were first introduced by Robertson
We establish a smaller subclass of SH, SHα (Sβ∗) := {f (z) = h (z) + g (z) ∈ SH : h (z)
Summary
Let S denote the class of functions of the form f(z) = z + An analytic function f(z) = z + ∑∞ n=2 anzn is said to be starlike of order β if zf (z) f (z) for which we write f(z) ∈ Sβ∗ ⊂ S, where β ∈ In [4], Hotta and Michalski denoted the class LH of all locally univalent and sense-preserving harmonic functions in the unit disk with h(0) = g(0) = h(0) − 1 = 0. In [5], the classes of starlike and convex functions of order β were first introduced by Robertson.
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