Better Uniform Approximation by New Bivariate Bernstein Operators

Abstract

In this paper we introduce new bivariate Bernstein type operators BnM,i(f; x, y), i = 1, 2, 3. The rates of approximation by these operators are calculated and it is shown that the errors are significantly smaller than those of ordinary bivariate Bernstein operators for sufficiently smooth functions.

Order of Approximation by a New Univariate Kantorovich Type Operator

“…Some new operators of type and their approximation degrees have been established in [20] by Gupta and Tachev. It is worth mentioning the recent work in this direction in [1], [2], [6], [13] and [14]. Recently, Kantorovich variants of a number of operators written in terms of the Choquet integral with respect to a monotone and submodular set function, Gal in [5] proved quantitative approximation estimates.…”