Statistical approximation properties of Stancu type q-Baskakov-Kantorovich operators

Abstract

In the present paper, we consider Stancu type generalization of Baskakov-Kantorovich operators based on the q-integers and obtain statistical and weighted statistical approximation properties of these operators. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type function are also established for said operators. Finally, we construct a bivariate generalization of the operator and also obtain the statistical approximation properties.

Approximation Properties of The Nonlinear Jain Operators

“…[13] introduced a generalization of Jain's operators based on a function ρ. Also, Bernstein and generalizations of Jain operators were studied by many authors (see [14]- [21].) The aim of this study is to introduce the nonlinear Jain operators of max-product type and estimate the rate of pointwise convergence of the operators.…”

Approximation Properties of Stancu-Type (p,q)-Baskakov Operators

“…Varied generalizations of some linear positive operators to the quantum calculus ( q -calculus) and their approximation results have been extensively investigated for three decades. Some generalizations of Baskakov operators based on qintegers can be read from [1][2][3]. Further, quantum calculus is extended to post-quantum calculus, displayed by ( , ) pq -calculus.…”