Some results of weighted Norlund-Euler statistical convergence

Abstract

In this paper we will define the new weighted statistically summbaility method, known as the weighted Norlund-Euler statistical convergence. We will show some properties of this method and we have proved Korovkin type theorem. Mathematics Subject Classification: 40G15

The rate of weighted Norlund–Euler statistical convergence

“…The idea of statistical convergence which is closely related to the concept of natural density or asymptotic density of a subset of the set of natural numbers N, was first introduced by Fast [7]. The idea of Norlund -Euler statistical convergence is defined by E. Aljimi, E. Hoxha and V. Loku [2] and generalizations of these methods are considered by E. Aljimi and V. Loku [21]. The weighted statistical convergence is defined by V. Karakaja and T.A.Chishti [3].…”

Weighted Norlund-Euler a-Statistical Convergence for Sequences of Positive Linear Operators

“…The authors of [18] established these types of approximation theorem in weighted p L spaces, where 1 p    , through A -summability which is stronger than ordinary convergence. For these types of approximation theorems and related concepts, one can be referred to [19][20][21][22][23][24][25][26][27][28][29] and references therein.…”

Steinhaus Type Theorem for Nörlund-(M, λn) and Nörlund-Euler-(M, λn) Methods of Summability in Non-Archimedean Fields

“…Loku and Aljimi introduced Nörlund-Euler-λ statistical convergence for reals in their study [5]. Many researchers studied Nörlund-Euler statistical convergence [2,3].…”