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In this paper we study a notion called (E, 1)(C, 1)−weighted statistical convergence and prove a Korovkin type approximation theorem. The rate of convergence for weighted statistical convergence is obtained. In the last section we also give Voronovskaya and Grüss-Voronovskaya type theorems and some illustrative numerical examples KEYWORDS

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

In this paper, we will show Tauberian conditions under which ordinary convergence of the sequence (𝑥𝑛) in 2-normed space 𝑋, follows from 𝑇 𝑝,𝑞 𝑛 -summability. In fact we give a necessary and sufficient Tauberian condition for this method of summability. Also, we prove that Tauberian Theorems for these summability methods are valid with Schmidt-type slowly oscillating condition as well as with Hardy-type "big O" condition.