Related papers: Korovkin-type Theorems and Approximation by Positi…
In this paper, using the concept of $A$-statistical convergence which is a regular (non-matrix) summability method, we obtain a general Korovkin type approximation theorem which concerns the problem of approximating a function $f$ by means…
We give some Korovkin-type theorems on convergence and estimates of rates of approximations of nets of functions, satisfying suitable axioms, whose particular cases are filter/ideal convergence, almost convergence and triangular…
This paper establishes an abstract Korovkin-type approximation theorem in general spaces, extending the framework of approximation theory to accommodate broader contexts. A critical result supporting this theorem is the proof that any…
Approximation theory has long been concerned with the development of positive linear operators that effectively approximate classes of functions. Among the most well-known results in this area are Korovkin-type approximation theorems, which…
We present Korovkin approximation theorems that incorporate summability methods. These result allows us to obtain a unified treatment of several previous results, focusing on the underlying structure and the properties that a summability…
We prove a Korovkin type approximation theorem via power series methods of summability for continuous $2\pi$-periodic functions of two variables and verify the convergence of approximating double sequences of positive linear operators by…
In this paper we prove analogues of Korovkin's theorem in the context of weakly nonlinear and monotone operators acting on Banach lattices of functions of several variables. Our results concern the convergence almost everywhere, the…
The classical as well as non commutative Korovkin-type theorems deal with convergence of positive linear maps with respect to modes of convergences such as norm convergence and weak operator convergence. In this article, Korovkin-type…
By extending the classical quantitative approximation results for positive and linear operators in $L^{p}([0, 1]), 1\le p \le +\infty$ of Berens and DeVore in 1978 and of Swetits and Wood in 1983 to the more general case of sublinear,…
In the present article, we propose the new class positive linear operators, which discrete type depending on a real parameters. These operators are similar to Jain operators but its approximation properties are different then Jain…
In this paper we deal with the convergence of sequences of positive linear maps to a (not assumed to be linear) isometry on spaces of continuous functions. We obtain generalizations of known Korovkin-type results and provide several…
This article provides a power series summability based Korovkin type approximation theorem for any fuzzy sequence of positive linear operators. Using the notion of fuzzy modulus of smoothness, we also derive an associated approximation…
In this paper we prove Korovkin type theorem for iterates of general positive linear operators $T:C\left[ 0,1\right] \rightarrow C\left[ 0,1\right] $ and derive quantitative estimates in terms of modulus of smoothness. In particular, we…
This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…
In this paper we introduce the Stancu type generalization of the q-Bernstein-Schurer-Kantorovich operators and examine their approximation properties. We investigate the convergence of our operators with the help of the Korovkin's…
The purpose of this paper is to study the approximation of vector valued mappings defined on a subset of a normed space. We investigate Korovkin-type conditions under which a given sequence of linear operators becomes a so-called…
The classical Korovkin theorem traditionally relies on the positivity of the underlying sequence of operators. However, in 1968, D. E. Wulbert established the first non-positive version. In this article, we generalize Wulbert's result to…
Our main aim is to investigate the approximation properties for the summation integral type operators in a statistical sense. In this regard, we prove the statistical convergence theorem using well known Korovkin theorem and the degree of…
In this paper we prove Korovkin type theorems for sequences of sublinear, monotone and weak additive operators acting on function spaces C(X); where X is a compact or a locally compact metric space. Our results are illustrated by a series…
This paper offers a newly created integral approach for operators employing the orthogonal modified Laguerre polynomials and P\u{a}lt\u{a}nea basis. These operators approximate the functions over the interval $[0,\infty)$. Further, the…