Korovkin type approximation theorems in weighted spaces via power series method

In this paper we consider power series method which is also member of the class of all continuous summability methods. We study a Korovkin type approximation theorem for a sequence of positive linear operators acting from a weighted space Cρ1 into a weighted space Bρ2 with the use of the power series method which includes both Abel and Borel methods. We also consider the rates of convergence of these operators. © 2018, Element D.O.O.. All rights reserved

SOME RESULTS FOR MAX-PRODUCT OPERATORS VIA POWER SERIES METHOD

WOS: 000442255800004In this paper, we obtain an approximation theorem by max-product operators with the use of power series method which is more effective than ordinary convergence and includes both Abel and Borel methods. We also estimate the error in this approximation. Finally, we provide an example which satisfies our theorem

Approximation by positive linear operators in modular spaces by power series method

WOS: 000414229600004In the present paper, we study the problem of approximation to a function by means of positive linear operators in modular spaces in the sense of power series method. Indeed, in order to get stronger results than the classical cases, we use the power series method which also includes both Abel and Borel methods. An application that satisfies our theorem is also provided

Some results for max-product operators via power series method

In this paper, we obtain an approximation theorem by max-product operators with the use of power series method which is more effective than ordinary convergence and includes both Abel and Borel methods. We also estimate the error in this approximation. Finally, we provide an example which satisfies our theorem. © 2018, Univerzita Komenskeho. All rights reserved

Generalized limits and sequence of matrices

Banach has proved that there exist positive linear regular functionals on m such that they are invariant under shift operator where m is the space of all bounded real sequences. It has also been shown that there exists positive linear regular functionals L on m such that L(?K) = 0 for every characteristic sequence ?K of sets, K, of natural density zero. Recently the comparison of such functionals and some applications have been examined. In this paper we define SB -limits and B-Banach limits where B is a sequence of infinite matrices. It is clear that if B= (A) then these definitions reduce to SA-limits and A-Banach limits. We also show that the sets of all SB -limits and Banach limits are distinct but their intersection is not empty. Furthermore, we obtain that the generalized limits generated by B where B is strongly regular is equal to the set of Banach limits. © 2019, Springer Nature Switzerland AG

KOROVKIN TYPE APPROXIMATION THEOREMS IN WEIGHTED SPACES VIA POWER SERIES

In this paper we consider power series method which is also member of the class of all continuous summability methods. We study a Korovkin type approximation theorem for a sequence of positive linear operators acting from a weighted space C-p1 into a weighted space B-p2 with the use of the power series method which includes both Abel and Borel methods. We also consider the rates of convergence of these operators

Statistical approximation properties of convolution operators for multivariables

In this paper, we study Korovkin type approximation results for a sequence of positive linear convolution operators defined on C([a,b]×[c,d]), the space of all continuous real valued functions on [a,b]×[c,d] with the use of A-statistical convergence. We also study rates of A-statistical convergence of these operators. © 2013 AIP Publishing LLC

Inclusion results on statistical cluster points

WOS: 000379043300005We study the concepts of statistical cluster points and statistical core of a sequence for A (lambda) methods defined by deleting some rows from a nonnegative regular matrix A. We also relate A (lambda)-statistical convergence to A (mu)-statistical convergence. Finally we give a consistency theorem for A-statistical convergence and deduce a core equality result