in this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$i$-statistical convergence and‎ ‎$i$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{n}$) and‎ ‎introduce the notions of $i$-statis...

In the present paper, we investigate the notion of I -statistical convergence and introduce I -st limit points and I -st cluster points of real number sequence and also studied some of its basic properties.

In the classical summability setting rates of summation have been introduced in several ways (see, e.g., [10], [21], [22]). The concept of statistical rates of convergence, for nonvanishing two null sequences, is studied in [13]. Unfortunately no single de...nition seems to have become the “standard” for the comparison of rates of summability transforms. The situation becomes even more uncharte...

An alternative approach, known today as the Bernstein polynomials, to Weierstrass uniform approximation theorem was provided by Bernstein. These basis polynomials have attained increasing momentum, especially in operator theory, integral equations and computer-aided geometric design. Motivated improvements of computational disciplines, we propose a new generalization Bernstein–Kantorovich opera...