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Abstract  

Analytic functions with bounded Mocanu variation generalize the concept of α-convexity in the unit disc. We introduce and study certain classes of such functions. Inclusion results are obtained and a sharp radius problem is solved.

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In the paper we prove that the complex analytic functions are (ordinarily) density continuous. This stays in contrast with the fact that even such a simple function asG:R2?R2,G(x,y)=(x,y 3 ), is not density continuous [1]. We will also characterize those analytic functions which are strongly density continuous at the given pointa ? C. From this we conclude that a complex analytic functionf is strongly density continuous if and only iff(z)=a+bz, wherea, b ? C andb is either real or imaginary.

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. 2 C otirlă , L. , A differential sandwich theorem for analytic functions defined by the integral operator , Stud. Univ. Babes–Bolyai Math. , 54 ( 2 ) ( 2009 ), 13 – 21

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