Shape preserving properties and monotonicity properties of the sequences of Choquet type integral operators

Abstract

In this paper, for the univariate Bernstein-Kantorovich-Choquet, Szasz-Kantorovich-Choquet, Baskakov-Kantorovich-Choquet and Bernstein-Durrmeyer-Choquet operators written in terms of the Choquet integrals with respect to monotone and submodular set functions, we study the preservation of the monotonicity and convexity of the approximated functions and the monotonicity of some approximation sequences.

Keywords

• monotone and submodular set function
• Choquet integral
• Bernstein-Kantorovich-Choquet polynomials
• Bernstein-Durrmeyer-Choquet polynomial
• Szasz-Kantorovich-Choquet operator
• Baskakov-Kantorovich-Choquet operator