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.
The estimates of approximation by using a new type of weighted modulus of continuity
In this paper, we introduce a new type modulus of continuity for function f belonging to a particular weighted subspace of C[0,~) and show that it has some properties of ordinary modulus of continuity. We obtain some estimates of approximation of functions with respect to a suitable weighted norm via the new type moduli of continuity. Finally, we give some examples.
Some results for modified Bernstein polynomials
Our aim is to find some properties for polynomials Lnf , defined as: (Lnf)(x) = (Bnf)(x)− x(1− x) 2(n− 1) (Bnf) ′′ (x), f ∈ C[0, 1], n = 2, 3, ... where Bnf is Bernstein polynomial corresponding to f . 2000 Mathematical Subject Classification: 41A17, 41A36.