On the Monotonicity of Positive Linear Operators

on the effect of linear & non-linear texts on students comprehension and recalling

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Stronger Maximal Monotonicity Properties of Linear Operators

On some fuzzy positive and linear operators

The purpose of this work is to show that fuzzy Bernstein-Stancu operators introduced in [3] satisfy an A-statistical version of fuzzy Korovkin theorem. Some properties of these operators are also proved. An example of new fuzzy positive and linear operators is presented.

Yet another look at positive linear operators, q-monotonicity and applications

For each q ∈ N0, we construct positive linear polynomial approximation operators Mn that simultaneously preserve k-monotonicity for all 0 ≤ k ≤ q and yield the estimate |f(x)−Mn(f, x)| ≤ cω λ 2 ( f, nφ(x) (φ(x) + 1/n) ) , for x ∈ [0, 1] and λ ∈ [0, 2), where φ(x) := √ x(1− x) and ω 2 is the second Ditzian-Totik modulus of smoothness corresponding to the “step-weight function” ψ. In particular, ...

On Linear Operators Preserving the Set of Positive Polynomials

Following the classical approach of Pólya-Schur theory [14] we initiate in this paper the study of linear operators acting on R[x] and preserving either the set of positive univariate polynomials or similar sets of non-negative and elliptic polynomials.