On multivariate Lupa 3 operators
This paper is primarily concerned with multivariate Lupa3 operator. We demonstrate that multivariate Lupa3 operator preserves the properties of the general function of modulus of continuity, Lipschitz's constant and order of a Lipschitz continuous function. Moreover, we obtain monotonicity of the multivariate Lupa3 operator under the condition that the original function is convex. Lastly, two modi ed extensions are constructed.
Bivariate Bernstein type operators
In this paper, we introduce bivariate extension of Bernstein type operators defined in 11. We show that these operators preserve some properties of the original function f, such as Lipschitz constant and monotonicity. Furthermore, we present the monotonicity of the sequence of bivariate Bernstein type operators for n when f is ?-convex.
Positive linear operators which preserve x2
A sequence of positive linear operators which approximate each continuous function on [0,1] while preserving the functione2(x) =x2 is presented. Quantitative estimates are given and are compared with estimates of approximation by Bernstein polynomials. Connections with summability are discussed.