The distance between two limit $q$-Bernstein operators

The distance between two limit q-Bernstein operators

For q ∈ (0, 1), let Bq denote the limit q-Bernstein operator. In this paper, the distance between Bq and Br for distinct q and r in the operator norm on C[0, 1] is estimated, and it is proved that 1 6 ‖Bq −Br‖ 6 2, where both of the equalities can be attained. To elaborate more, the distance depends on whether or not r and q are rational powers of each other. For example, if rj 6= qm for all j,...

q−BERNSTEIN-SCHURER-KANTOROVICH TYPE OPERATORS

The aim of this paper is to present a Stancu type Kantorovich modification of q−BernsteinSchurer operators introduced by Muraru [22] and modified by Ren and Zeng [29]. Here, we obtain a convergence theorem by using the well known Bohman-Korovkin criterion and find the estimate of the rate of convergence by means of modulus of continuity and Lipschitz function for these operators. Also, we estab...

On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators

In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...

A Survey of Results on the Limit q-Bernstein Operator

The limit q-Bernstein operator B q emerges naturally as a modification of the Szász-Mirakyan operator related to the Euler distribution, which is used in the q-boson theory to describe the energy distribution in a q-analogue of the coherent state. At the same time, this operator bears a significant role in the approximation theory as an exemplarymodel for the study of the convergence of the q-o...

Modified (p,q)-Bernstein-Schurer operators and their approximation properties