On Kantorovich Process of a Sequence of the Generalized Linear Positive Operators

Abstract

We define the Kantorovich variant of the generalized linear positive operators introduced by Ibragimov and Gadjiev in 1970. We investigate direct approximation result for these operators on p-weighted integrable function spaces and also estimate their rate of convergence for absolutely continuous functions having a derivative coinciding a.e., with a function of bounded variation.

Keywords:

• Bounded variation
• Derivatives of bounded variation
• Kantorovich-type operators
• Linear positive operators
• Rate of convergence
• Total variation
• Weighted approximation

AMS Subject Classification:

• 41A30
• 41A36
• 41A25

ACKNOWLEDGMENTS

This work is dedicated to Professor Akif D. Gadjiev on the occasion of his 70th birthday. The authors are thankful to the reviewer for making valuable suggestions, leading to a better presentation of the paper.