We obtain estimates for the transformation of the second order modulus of continuity by positive linear operators which satisfy certain conditions, which are common to a large class of approximation operators.

An estimation of approximation of continuous functions by positive linear operators in weighted norm using the weighted modulus of continuity is established. Application of the main result to the known Gadjiyev∗ -Ibragimov operators is given.

The spectral bound, s(αA + βV), of a combination of a resolvent positive linear operator A and an operator of multiplication V, was shown by Kato to be convex in β ∈ R. Kato's result is shown here to imply, through an elementary "dual convexity" lemma, that s(αA + βV) is also convex in α > 0, and notably, ∂s(αA + βV)/∂α ≤ s(A). Diffusions typically have s(A) ≤ 0, so that for diffusions with spa...

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...

Recently Deo N.et.al.1. INTRODUCTION Recently Deo N.et.al. [1] Introduced new Bernstein type special operators defined as, Again Deo N.et.al. [1] gave the integral modification of the operators (1.1) which are defined as , and prove some approximation results on the operators (1.2). Singh S.P. [4] studied some approximation results on a sequence of Szȧ sz type operators defined as, which map th...

This survey paper contains a detailed self-contained introduction to Korovkin-type theorems and to some of their applications concerning the approximation of continuous functions as well as of L-functions, by means of positive linear operators. The paper also contains several new results and applications. Moreover, the organization of the subject follows a simple and direct approach which quick...

the main result of this article is that for collections of entry-wise non-negative matrices the property of possessing a standard triangularization is stable under approximation. the methodology introduced to prove this result allows us to offer quick proofs of the corresponding results of [b. r. yahaghi, near triangularizability implies triangularizability, canad. math. bull. 47, (2004), no. 2...