Korovkin Second Theorem via B-Statistical A-Summability

Abstract EN

Korovkin type approximation theorems are useful tools to check whether a given sequence (Ln)n≥1 of positive linear operators on C[0,1] of all continuous functions on the real interval [0,1] is an approximation process.

That is, these theorems exhibit a variety of test functions which assure that the approximation property holds on the whole space if it holds for them.

Such a property was discovered by Korovkin in 1953 for the functions 1, x, and x2 in the space C[0,1] as well as for the functions 1, cos, and sin in the space of all continuous 2π-periodic functions on the real line.

In this paper, we use the notion of B-statistical A-summability to prove the Korovkin second approximation theorem.

We also study the rate of B-statistical A-summability of a sequence of positive linear operators defined from C2π(ℝ) into C2π(ℝ).