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    STUDIA MATHEMATICA - Issue no. 3 / 2010  

Authors:  PETRU T. MOCANU.
  Abstract:  Let C : z = z(t), t Є [a, b], be a smooth Jordan curve of the class C2 and let f be a complex univalent function of the class C1 in a domain which contains the curve C together with its interior. Suppose that the origin lies inside of C and f(0) = 0. Let Γ = f(C) and suppose that Γ is starlike with respect to the origin. Let consider the radius vector from 0 to a point w Є Γ and let be the outer normal to Γ at the point w = f[z(t)]. Let denote by the angle between and and consider the vector starting from w, such that sin Ψ = γ sin ω, where and γ is a positive number. We say that the starlike curve Γ = f(C) has the regular refraction property, with index γ, if the argument of the vector is an increasing function of t Є [a, b]. The concept of regular refraction property was introduced in [2] and developed in [3], [4], [5], [6] and [7]. We mention that this concept is closed to the concept of α-convexity introduced in [1]. In this paper we continue to study this geometric property by introducing the concept of regular refraction interval of a given function. We also give a significant example.

Key words and phrases. Starlike functions, regular refraction

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