Abstract
In the present paper we investigate a class of harmonic mappings for which the second dilatation is a close-to-convex function of complex order b, $b\in\mathbb{C} / \{ 0 \}$ (Lashin in Indian J. Pure Appl. Math. 34(7):1101-1108, 2003).
Highlights
A planar harmonic mapping in the open unit disc D = {z||z| < } is a complex-valued harmonic function f which maps D onto some planar domain f (D)
An elegant and complete account of the theory of planar harmonic mappings is given in Duren?s monograph [ ]
Throughout this paper, we restrict ourselves to the study of sense-preserving harmonic mappings
Summary
The class of all sense-preserving harmonic mappings in the open unit disc D with a = b = and a = is denoted by SH. Let s(z) be an element of A, s(z) is said to be close-to-convex of complex order b, b ∈ C/{ } if and only if there exists a function φ(z) ∈ C(b) satisfying the condition s (z) The class of such functions is denoted by CC(b). A planar harmonic mapping in the open unit disc D is a complex-valued harmonic function f , which maps D onto some planar domain f (D).
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