ON THE DEGREE OF APPROXIMATION OF THE HERMITE AND HERMITE-FEJER INTERPOLATION

Here we find the order of convergence of the Hermite and Hermite-Fejer interpolation polynomials constructed on the zeros of (1−x2)Pn(x) where Pn(x) is the Legendre polynomial of degree n with normalization Pn(1)=1.

If the ce a [p-1,p), p 3 (p integer) the necsy d sufficient conditions for the vMidity of (1.9) is given by () Here Ra'a)(f,x) is the lynomiM of de 2n + 3 satisfying the interpolatory conditions (1.7) on the zeros of ultrphericM polynomiM.
For Rn(f,x) satisfying the interpolatory conditions (1.7) on the zeros of (I -x2)Pn(x) we prove the following: THEOREM 1.
2. PRELIMINARIES.In this section we state a few known results which we shall use later on.

Call for Papers
Thinking about nonlinearity in engineering areas, up to the 70s, was focused on intentionally built nonlinear parts in order to improve the operational characteristics of a device or system.Keying, saturation, hysteretic phenomena, and dead zones were added to existing devices increasing their behavior diversity and precision.In this context, an intrinsic nonlinearity was treated just as a linear approximation, around equilibrium points.Inspired on the rediscovering of the richness of nonlinear and chaotic phenomena, engineers started using analytical tools from "Qualitative Theory of Differential Equations," allowing more precise analysis and synthesis, in order to produce new vital products and services.Bifurcation theory, dynamical systems and chaos started to be part of the mandatory set of tools for design engineers.
This proposed special edition of the Mathematical Problems in Engineering aims to provide a picture of the importance of the bifurcation theory, relating it with nonlinear and chaotic dynamics for natural and engineered systems.Ideas of how this dynamics can be captured through precisely tailored real and numerical experiments and understanding by the combination of specific tools that associate dynamical system theory and geometric tools in a very clever, sophisticated, and at the same time simple and unique analytical environment are the subject of this issue, allowing new methods to design high-precision devices and equipment.
Authors should follow the Mathematical Problems in Engineering manuscript format described at http://www .hindawi.com/journals/mpe/.Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http:// mts.hindawi.com/according to the following timetable: ) (xxk)P'n(xk)

11 THEOREM
A. Let f {5 C[-1,1].In the case when a E [--,) the necessary and sufficient conditions for ji R(na'o')(f,x) f(x)II o (1.9) is given by and lim

First
Round of Reviews March 1, 2009