Statistical Convergence of Bernstein Operators

Abstract

The Bernstein operator is one of the important topics of approximation theory in which it has been studied in great details for a long time. The aim of this paper is to study the statistical convergence of sequence of Bernstein polynomials. In this paper, we introduce the concepts of statistical convergence of Bernstein polynomials and V B −summability and related theorems. We also study Korovkin type-convergence of Bernstein polynomials.

Pascal Triple Entire Sequence Space of Fibonacci Binomial Matrix on Rough Statistical Convergence And Its Rate

“…For example, we can form three types of matrix; symmetric, lower triangular and upper triangular; for any integer . The symmetric Pascal matrix of order is defined by (6) We can define the lower triangular Pascal matrix of order by (7) and the upper triangular Pascal matrix of order is defined by (8) We know that for any positive integer . (i).…”

The (p; q)-Bernstein-Stancu operator of rough statistical convergence on triple sequence

“…A triple sequence (real or complex) can be defined as a function x : N 3 → R (C) , where N, R and C denote the set of natural numbers, real numbers and complex numbers respectively. The different types of notions of triple sequence was introduced and investigated at the initial by Sahiner et al [11,12], Esi et al [2,3,4,5], Datta et al [6], Subramanian et al [13], Debnath et al [7] and many others.…”

Lacunary statistical convergence of Bernstein operator sequences

“…In this case, we write as -lim ( , ) = ( ) or ( , ) ( ) (Esi et al, 2016). Let be a continuous function defined on the closed interval [0,1].…”

“…Let be a continuous function defined on the closed interval [0,1]. Then a sequence of Bernstein polynomials ( ( , )) is said to be strongly Cesàro summable of -summable to ( ) if (Esi et al, 2016):…”