Tchebycheff approximation in several variables

Best Approximation of Monomials in Several Variables

For a monomial x in d variables, the problem of best approximation to x by polynomials of lower degrees is studied on the unit sphere, the unit ball and the standard simplex. For the uniform norm we discuss what is known in d = 2, for which complete solutions are known, and in d ≥ 3 for which only a few cases have been successfully solved. For the L norm, we present the complete solution, inclu...

Tchebycheff Approximation in a Compact Metric Space

Generalized translation operator and approximation in several variables

Generalized translation operators for orthogonal expansions with respect to families of weight functions on the unit ball and on the standard simplex are studied. They are used to define convolution structures and modulus of smoothness for these regions, which are in turn used to characterize the best approximation by polynomials in the weighted Lp spaces. In one variable, this becomes the gene...

Approximation of smooth periodic functions in several variables

Approximately generalized additive functions in several variables

The goal of  this paper is to investigate the solutionand stability in random normed spaces, in non--Archimedean spacesand also in $p$--Banach spaces and finally the stability using thealternative fixed point of generalized additive functions inseveral variables.