ON THE APPROXIMATION OF CONTINUOUS FUNCTIONS OF TWO VARIABLES BY ALGEBRAIC POLYNOMIALS,

Abstract

The following theorem of S. A. Telyakovskii is generalized in the present paper for the two-dimensional case: for every function f(x) continuous on the segment (-1,1) and for any positive n one can construct an algebraic polynomial g sub n(f;x) of degree not higher than n such that for all x epsilon (-1,1) the inequality the absolute value of (f(x)-(g sub n)(f;x)) = or < (A sub1) omega (f;(the square root of (1-x squared))/n) is fulfilled, where A sub 1 is an absolute constant and omega (f) is the continuity modulus of the function f. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 09, 1969
Accession Number
AD0690329

Entities

People

  • V. N. Malozemov

Organizations

  • Johns Hopkins University Applied Physics Laboratory

Tags

DTIC Thesaurus Topics

  • Continuity
  • Inequalities
  • Mathematical Analysis
  • Mathematics
  • Polynomials
  • Square Roots
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Approximation Theory.