On a discrete Korovkin theorem

Variations on a Theorem of Korovkin

Matrix Summability and Korovkin Type Approximation Theorem on Modular Spaces

In this paper, using a matrix summability method we obtain a Korovkin type approximation theorem for a sequence of positive linear operators defined on a modular space.

Korovkin Second Theorem via B-Statistical A-Summability

and Applied Analysis 3 f continuous on R. We know that C(R) is a Banach space with norm 󵄩󵄩󵄩f 󵄩󵄩󵄩∞ := sup x∈R 󵄨󵄨󵄨f (x) 󵄨󵄨󵄨 , f ∈ C (R) . (12) We denote by C 2π (R) the space of all 2π-periodic functions f ∈ C(R) which is a Banach space with 󵄩󵄩󵄩f 󵄩󵄩󵄩2π = sup t∈R 󵄨󵄨󵄨f (t) 󵄨󵄨󵄨 . (13) The classical Korovkin first and second theorems statewhatfollows [15, 16]: Theorem I. Let (T n ) be a sequence of p...

A - Statistical extension of the Korovkin type approximation theorem

Let A = (a jn) be an infinite summability matrix. For a given sequence x := (xn), the A-transform of x, denoted by Ax := ((Ax) j), is given by (Ax) j = ∑n=1 a jnxn provided the series converges for each j ∈ N, the set of all natural numbers. We say that A is regular if limAx = L whenever limx = L [4]. Assume that A is a non-negative regular summability matrix. Then x = (xn) is said to be A-stat...

Korovkin type theorem in the space C̃ b [ 0 , ∞ )

A Korovkin type theorem is established in the space C̃b[0,∞) of all uniformly continuous and bounded functions on [0,∞) for a sequence of positive linear operators, the approximation error being estimated with the aid of the usual modulus of continuity. As applications we obtain quantitative results for q-Baskakov operators. Mathematics Subject Classification (2010): 41A36, 41A25.