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,....