Higher order fuzzy Korovkin theory via inequalities
Here is studied with rates the fuzzy uniform and Lp, P ≥ 1, convergence of a sequence of fuzzy positive linear operators to the fuzzy unit operator acting on spaces of fuzzy differentiable functions. This is done quantitatively via fuzzy Korovkin type inequalities involving the fuzzy modulus of continuity of a fuzzy derivative of the engaged function. From there we deduce general fuzzy Korovkin type theorems with high rate of convergence. The surprising fact is that basic real positive linear operator simple assumptions enforce here the fuzzy convergences. At the end we give applications. Our results are univariate and multivariate. The assumptions are minimal and natural fulfilled by almost all example - fuzzy positive linear operators. © Dynamic Publishers, Inc.
Communications in Applied Analysis
Anastassiou, G. (2006). Higher order fuzzy Korovkin theory via inequalities. Communications in Applied Analysis, 10 (2-3), 359-392. Retrieved from https://digitalcommons.memphis.edu/facpubs/4897