Subclass of Harmonic Univalent Functions with Respect to 2k-Symmetric Conjugate Points
نویسندگان
چکیده
A continuous function f = u + iv is a complex valued harmonic function in a complex domain C if both u and v are real harmonic in C. In any simply connected domain D ⊂ C we can write f(z) = h + g, where h and g are analytic in D. We call h the analytic part and g the co-analytic part of f . A necessary and sufficient condition for f to be locally univalent and sense-preserving in D is that |h′(z)| > |g′(z)| in D. See Clunie and Sheil-Small (see [1]). Denote by SH the class of functions f = h+g that are harmonic univalent and sense-preserving in the unit disk U = {z : |z| < 1} for which f(0) = h(0) = fz(0)− 1 = 0. For f = h + g ∈ SH we may express the analytic functions h and g as
منابع مشابه
Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points
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