On circularly symmetric functions
Journal Title: Journal of Mathematics and Applications - Year 2014, Vol 37, Issue
Abstract
Let D ⸦ C and 0 ∈ D. A set D is circularly symmetric if for each [formula] a set [formula] is one of three forms: an empty set, a whole circle, a curve symmetric with respect to the real axis containing ϱ. A function f ∈ A is circularly symmetric if f(Δ) is a circularly symmetric set. The class of all such functions we denote by X. The above definitions were given by Jenkins in [2]. In this paper besides X we also consider some of its subclasses: X(λ) and Y ∩ S* consisting of functions in X with the second coefficient fixed and univalent starlike functions respectively. According to the suggestion, in Abstract we add one more paragraph at the end of the section: For X(λ) we find the radii of starlikeness, starlikeness of order α, univalence and local univalence. We also obtain some distortion results. For Y ∩ S* we discuss some coefficient problems, among others the Fekete-Szeg ö ineqalities.
Authors and Affiliations
Leopold Koczan, Paweł Zaprawa
Keywords
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