Triangular A-Statistical Approximation by Double Sequences of Positive Linear Operators

Korovkin type approximation via triangular A−statistical convergence on an infinite interval

“…Recently, Bardaro et al [5] introduced an approximation theorem with the help of the notion of new statistical convergence called triangular A−statistical convergence. Let C * (D) be a Banach space of all real-valued continuous functions on D := [0, ∞) × [0, ∞) with the property that lim (u,v)→(∞,∞) f (u, v) exists and is finite.…”

“…Definition 1.1 [5] Let A = (a i,j ) be a nonnegative regular summability matrix, K ⊂ N 2 be a nonempty set, and for every i ∈ N,…”

Abstract Korovkin-type theorems in the filter setting with respect to relative uniform convergence

“…There have been also several studies on Korovkin-type theorems related to convergence associated with summability methods, statistical and filter convergence (see e.g., [5,8,9,29,[32][33][34]49]).…”

Abstract Korovkin Theorems via Relative Modular Convergence for Double Sequences of Linear Operators

“…Many researchers studied some versions of this theorem in different spaces and Bardaro and Mantellini studied this theorem on modular spaces which is the natural generalization of L p (p > 0), Orlicz, Lorentz, and Köthe spaces ( [5]) and so on( [7,8]). In addition, general versions of the Korovkin theorem were studied in which a various kind of convergence methods is used, particularly statistical convergence methods( [2,3,14,22]). More recently, Demirci and Orhan ([9]) have introduced statistical relative uniform convergence of single sequences by using the notions of the natural density and the relative uniform convergence.…”