\(\mathcal I\)-convergence of positive linear operators on \(L_p\) weighted spaces. (English) Zbl 1134.41004
Summary: Using the concept of \(\mathcal I\)-convergence we prove a Korovkin type approximation by means of positive linear operators defined on the weighted space \(L_{p,\omega}(\mathbb R)\). Also we state its \(n\)-dimensional analogue for the weighted space \(L_{p,\Omega}(\mathbb R^n)\). Also we display an example such that our method of convergence is stronger than the usual convergence in the weighted spaces \(L_{p,\omega}(\mathbb R)\) and \(L_{p,\Omega}(\mathbb R^n)\).
MSC:
| 41A10 | Approximation by polynomials |
| 41A25 | Rate of convergence, degree of approximation |
| 41A36 | Approximation by positive operators |
| 40A05 | Convergence and divergence of series and sequences |
| 40A30 | Convergence and divergence of series and sequences of functions |
