The paper centers around a pair of sequences of linear positive operators. The former has the degree of exactness one and the latter has its degree of exactness null, but, as a novelty, it reproduces the third test function of Korovkin theorem. Quantitative estimates of the rate of convergence are given in different function spaces traveling from classical approximation to approximation in abst...

A = (ank) be a regular summability matrix. In the present paper we deal with subspaces of space A?statistically convergent sequences obtained by rate at which A?statistical limit tends to zero. We prove that sequence is A?strongly if and only it A?uniformly integrable o (an) where positive nonincreasing sequence. also make link between A?strong convergence A?distributional (an). Finally, as an ...

In this article, we define a new operator by Appell polynomials. Primarily, some equations are obtained using the properties of Korovkin theorem. Later, convergence sequence that have defined has been proved and approximation results given theory.

The main results of this paper offer sufficient conditions in order that an approximate lower Hermite–Hadamard type inequality implies an approximate Jensen convexity property. The key for the proof of the main result is a Korovkin type theorem.

The main purpose of this paper is to introduce some approximation properties a Kantorovich kind q-Bernstein operators related Bézier basis functions with shape parameter . Firstly, we compute basic results such as moments and central moments, derive the Korovkin type theorem for these operators. Next, estimate order convergence in terms usual modulus continuity, belong Lipschitz-type class Peet...

*Correspondence: [email protected] 2Department of Mathematics, Gauhati University, Guwahati, India Full list of author information is available at the end of the article Abstract The notion of statistical weighted B-summability was introduced very recently (Kadak et al. in Appl. Math. Comput. 302:80–96, 2017). In the paper, we study the concept of statistical deferred weighted B-summ...