In the current research, we investigate and establish Korovkin-type approximation theorems for linear operators defined on space of all $% 2\pi $-periodic real valued continuous functions %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{2}$ by means $\mathcal{A}$-summation process via statistical convergence with respect to power series method. We demonstrate an example how our ...

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...

Korovkin-type theorems in modular spaces and applications C. Bardaro ∗ A. Boccuto † X. Dimitriou ‡ I. Mantellini § Abstract We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results even with respect to an axiomatic convergence, whose...

In this paper, we establish a link between the Szász-Durrmeyer type operators and multiple Appell polynomials. We study a quantitative-Voronovskaya type theorem in terms of weighted modulus of smoothness using sixth order central moment and Grüss-Voronovskaya type theorem. We also establish a local approximation theorem by means of the Steklov means in terms of the first and the second order mo...

We study the optimal and superoptimal Frobenius operators in a general matrix vector space and in particular in the multilevel trigonometric matrix vector spaces, by emphasizing both the algebraic and geometric properties. These general results are used to extend the Korovkin matrix theory for the approximation of block Toeplitz matrices via trigonometric vector spaces. The abstract theory is t...