Lacunary statistical convergence of Bernstein operator sequences

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. Recently the statistical convergence of Bernstein operators was studied. In this paper, by using the concept of natural density and lacunary sequences we first introduce the notion of lacunary statistical convergence of a sequence of Bernstein polynomials. Next we apply this notion to -summability. We also investigate some inclusion relations related to these concepts.

On the Entire Paranormed Triple Sequence Spaces of Defined by Binomial Poisson Matrix

“…, x × × →      where ,   and  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 [1,2], Esi et al [3,4,5,6,7,8], Dutta et al [9], Subramanian et al [10], Debnath et al…”

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).…”

“…(iii) Let be the symmetric Pascal matrix of order defined by (6), then is similar to its inverse . (iv) Let be the lower triangular Pascal matrix of order defined by (7), then . We wish to introduce the Pascal sequence spaces and as the set of all sequences such that transforms of them are in the spaces and , respectively, that is and We may redefine the spaces , as follows: , .…”

On rough convergence of triple sequence spaces of Bernstein-Stancu operators of fuzzy numbers defined by a metric function

“…A triple sequence (real or complex) can be defined as a function x : N × N × N → 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 [15,16], Esi et al [3][4][5][6][7][8], Datta et al [9],Subramanian et al [17], Debnath et al [10] and many others.…”