General Mathematics, Vol. 9,nr. 3-4, 2001
Abstract:
Using the differential operator Dn f introduced by G.
Sălăgean and the results given in
[2] and [3] on the several
types of close-to-convex functions, in this paper I define new
sets of univalent functions called n--uniformly
close-to-convex
with respect to a convex domain. In the definition of this
functions it is specified which is the convex domain, symmetrical
to the real axis, for example: elliptic, parabolic, hyperbolic
region, or half plane. A certain analogy with the uniformly convex
functions and with the functions of the class Sp
defined by
Goodman and by Frode Ronning respectively, justifies the name
"uniformly close-to-convex".
In the second part, the intermediate classes of Mocanu type are
also being defined.
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