Functions and Analysis

2311 Submissions

[2] viXra:2311.0093 [pdf] submitted on 2023-11-20 20:23:34

Extension Formulas and Norm Inequalities in Sobolev Hilbert Spaces

Authors: Saburou Saitoh
Comments: 11 Pages.

In this note, we shall consider extension formulas and norm inequalities for some typical Sobolev Hilbert spaces. We see many related openproblems.
Category: Functions and Analysis

[1] viXra:2311.0036 [pdf] submitted on 2023-11-08 01:11:54

Roots of Real Polynomial Functions and of Real Functions

Authors: Juan Jorge Isaac Lopez
Comments: 4 Pages.

The Newton-Raphson method is the most widely used numerical calculation method to determine the roots of Real polynomial functions, but it has the drawback that it does not always converge. The method proposed in this work establishes the convergence condition and the development of its application, and therefore will always converge towards the roots of the function. This will mean a conclusive advance for the determination of roots of Real polynomial functions. According to interpretation of the Abel-Ruffini theorem, the roots of polynomial functions of degree greater than 4 can only be determined by numerical calculation.
Category: Functions and Analysis