On Kantorovich modification of ( p , q ) $( p,q ) $ -Baskakov operators

Abstract

Abstract The concern of this paper is to introduce a Kantorovich modification of ( p , q ) $( p,q ) $ -Baskakov operators and investigate their approximation behaviors. We first define a new ( p , q ) $( p,q ) $ -integral and construct the operators. The rate of convergence in terms of modulus of continuities, quantitative and qualitative results in weighted spaces, and finally pointwise convergence of the operators for the functions belonging to the Lipschitz class are discussed.

Keywords

• ( p , q ) $( p,q )$ -integers
• ( p , q ) $( p,q )$ -integral
• ( p , q ) $( p,q )$ -Baskakov-Kantorovich operators
• weighted approximation
• rate of convergence