Periodic Korovkin Theorem via $P_{p}^{2}$-Statistical $\mathcal{A}$-Summation Process

Korovkin-Type Theorems in Weighted Lp-Spaces via Summation Process

Korovkin-type theorem which is one of the fundamental methods in approximation theory to describe uniform convergence of any sequence of positive linear operators is discussed on weighted Lp spaces, 1 ≤ p < ∞ for univariate and multivariate functions, respectively. Furthermore, we obtain these types of approximation theorems by means of A-summability which is a stronger convergence method than ...

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...

Generalization of Statistical Korovkin Theorems

The classical Korovkin theory enables us to approximate a function by means of positive linear operators (see, e.g., [1– 3]). In recent years, this theory has been quite improved by some efficient tools inmathematics such as the concept of statistical convergence from summability theory, the fuzzy logic theory, the complex functions theory, the theory of q-calculus, and the theory of fractional...

Variations on a Theorem of Korovkin