A-Statistical convergence of approximating operators

Abstract

Abstract. In this paper we provide various approximation results concerning the classical Korovkin theorem via A -statistical convergence. We also study the rates of A -statistical convergence of approximating positive linear operators and give some examples.

Rate of convergence of Szász-beta operators based on q-integers

“…Following [29], we say that a sequence Finally, taking the in mum over all g ∈ W on the right side of above inequality and using (16)- (17) we obtain | Bn,q(f ; x) − f (x)| ≤ Cω (f , ξn(x), which completes the proof of the theorem.…”

Four-dimensional matrix transformation and A-statistical fuzzy Korovkin type approximation

“…Various ways of defining rates of convergence in the A-statistical sense for two-dimensional summability matrices were introduced in [7]. In a similar way, we obtain fuzzy approximation theorems based on A-statistical rates for four-dimensional summability matrices.…”

Approximation in statistical sense to n-variate B-continuous functions by positive linear operators

“…However, this theory was generalized by using the notion of B-continuity instead of the ordinary continuity ( [4,5,6]). Furthermore, in recent years, with the help of the concept of statistical convergence, various statistical approximation results have been proved [1,2,13,14,15,18]. Recall that every convergent sequence (in the usual sense) is statistically convergent but its converse is not always true.…”