Quantitative results for positive linear operators which preserve certain functions

Linear operators that preserve some test functions

The paper centers around a pair of sequences of linear positive operators. The former has the degree of exactness one and the latter has its degree of exactness null, but, as a novelty, it reproduces the third test function of Korovkin theorem. Quantitative estimates of the rate of convergence are given in different function spaces traveling from classical approximation to approximation in abst...

Linear Operators Which Preserve Pairs on Which the Rank Is Additive

Let A and B be m n matrices. A linear operator T preserves the set of matrices on which the rank is additive if rank(A + B) = rank(A) + rank(B) implies that rank(T (A) + T(B)) = rankT (A) + rankT (B). We characterize the set of all linear operators which preserve the set of pairs of n n matrices on which the rank is additive.

On Composition Operators Which Preserve Bmo

Q |f − fQ|dx < ∞, (1) where |Q| is the n-dimensional Lebesgue measure of Q, fQ = |Q|−1 ∫ Q fdx, and the supremum is taken over all closed cubes Q ⊂ D with sides parallel to the coordinate axes. Let D and D′ be subdomains of Rm and Rn, m, n ≥ 1, respectively. We say that a map F : D → D′ is measurable if F−1(E) is measurable for each measurable subset E of D′. We say that a measurable map F : D ...

Approximation of functions of two variables by certain linear positive operators

Abstract. We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an rth order generalization of these operators and observe its approximation properties. Furthermore, we study ...

Subordination and Super Ordination Results Involving Certain Convolution Operators