There exists a family of isometric immersions of [R.sup.2] into [R.sup.4] with vanishing normal curvature, each of which depends on four real parameters s, a, b, c and an analytic function
w on [R.sup.2].
The problem of finding coefficient bounds, distortion bounds, extreme points, convex linear combinations, starlikeness and convexity properties of analytic function
are the most fundamental problems in Geometric Function Theory.
The remainder term of the Kronrod extension of the generalization of Micchelli-Rivlin quadrature formula for analytic functions
. Let f be an analytic function
on a domain D which contains the interval [-1,1] in its interior, and let [GAMMA] be a simple closed curve in D surrounding [-1,1].
A weighted composition operator [C.sub.[psi],[phi]] on [F.sup.2] with y an analytic function
on [C.sup.N] and [phi] an analytic self-map of [C.sup.N] is defined as
Since we are working with complex numbers, we will be dealing with analytic functions
. Supposing g(z) is an analytic function
and a is in its domain, we can write
and consider the starlike analytic function
[phi] (z) = z + [z.sup.n]/n; n [greater than or equal to] 2 in D.
Because z([zeta]) is an analytic function
, the expression z([zeta])/[bar.z'([zeta])] must be an analytic function
in ring D".
Very recently, the upper bounds of [H.sub.2](2) for some specific analytic function
classes were discussed by Deniz et al.
Define the analytic function
p : D [right arrow] C by
The new Global Business Innovation Department will integrate the analytic function
of the market/technology needs belonging to the Technology & Innovation Headquarters' Business Process Innovation Department and the region-specific needs survey functions of the Global Business Planning & Operations Headquarters' International Business Promotion Department.
is an analytic function
in U with positive real part, then
where [f.sub.k]([r.sub.k-1], [r.sub.k-2], ..., [r.sub.1], [r.sub.0], [theta]) is analytic function
about [r.sub.k-1], [r.sub.k-2],..., [r.sub.1], [r.sub.0], cos([theta]), sin([theta]), k = 0,1,2,....