In this paper, using equi-ideal convergence, we introduce a non-trivial generalization of the classical and the statistical cases of the Korovkin approximation theorem. We also compute the rates of equi-ideal convergence of sequences of positive linear operators. Furthermore, we obtain a Voronovskaya-type theorem in the equi-ideal sense for a sequence of positive linear operators constructed by...

In this paper, we introduce the concept of triangular A-statistical relative convergence for double sequences functions defined on a compactsubset real two-dimensional space. Based upon new convergencemethod, prove Korovkin-type approximation theorem. Finally, give some further developments.

In the present paper a Korovkin-type theorem is proposed for the approximation operators defined by the inverse Ftransforms. These results allow us to choose between a variety of shapes to be used as atoms of the fuzzy partitions used within the F-transform’s framework. In this way we can enlarge considerably the class of F-transforms proposed recently by I. Perfilieva. The new fuzzy partitions...

In this paper, we define the concept of statistical relative uniform convergence deferred Nörlund mean and prove a general Korovkin-type approximation theorem by using method. As an application, use classical Bernstein polynomials for defining operator that satisfies our new but does not satisfy given before. Additionally, estimate rate approximating positive linear operators means modulus cont...

In this paper, we introduce the concepts of weighted ideal statistical convergence or SN (I)-convergence and I − (N, pn)-summability. We also establish the relations between our new methods. Further, we determine a Korovkin type approximation theorem through I − (N, pn)-summability. −−−−−−−−−−−−−−−−−−−−−−−−−−−−

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...

In this paper, we introduce a new family of generalized Bernstein-Schurer operators and investigate some approximation properties these operators. We obtain uniform result using the well-known Korovkin theorem give degree via second modulus smoothness. Also, present Voronovskaya Grüss-Voronovskaya type results for

In the present paper, we study a Kantorovich type generalization of Meyer-König and Zeller type operators via generating functions. Using Korovkin type theorem we first give approximation properties of these operators defined on the space C [0, A] , 0 < A < 1. Secondly, we compute the rate of convergence of these operators by means of the modulus of continuity and the elements of the modified L...

In this paper, using the concept of statistical A-summability which is stronger than the A-statistical convergence, we prove a Korovkin type approximation theorem for sequences of positive linear operator defined on C∗(R) which is the space of all 2π-periodic and continuous functions on R, the set of all real numbers. We also compute the rates of statistical A-summability of sequence of positiv...

Our aim is to define modified Sz?sz type operators involving Charlier polynomials and obtain some approximation properties. We prove results on the order of convergence by using modulus smoothness Peetre?s K-functional. also establish Voronoskaja theorem for these operators. Moreover, we a Korovkin via q-statistical convergence.