Ahlfors-Schwarz lemma and curvature
In this paper an alternative characterization of the class of functions called k -uniformly convex is found. Various relations concerning connections with other classes of univalent functions are given. Moreover a new class of univalent functions, analogous to the ’Mocanu class’ of functions, is introduced. Some results concerning this class are derived.
MSC 2010: 30C45Applying the Bernardi integral operator, an interesting convolution integral is introduced. The object of the present paper is to derive some convolution integral properties of functions f(z) to be in the subclasses of the classes S*(α) and Κ(α) by making use of their coefficient inequalities.
We give a new proof of a Phragmén Lindelöf theorem due to W.H.J. Fuchs and valid for an arbitrary open subset of the complex plane: if is analytic on , bounded near the boundary of , and the growth of is at most polynomial then either is bounded or for some positive and has a simple pole.
We introduce and study some new subclasses of starlike, convex and close-to-convex functions defined by the generalized Bessel operator. Inclusion relations are established and integral operator in these subclasses is discussed.