Equivalent theorem of approximation by linear combination of weighted Baskakov–Kantorovich operators in Orlicz spaces

Abstract

Abstract In this paper, we introduce the Orlicz space corresponding to the Young function and, by virtue of the equivalent theorem between the modified K-functional and modulus of smoothness, establish the direct, inverse, and equivalent theorems for linear combination of the Jacobi weighted Baskakov–Kantorovich operators in the Orlicz spaces.

Keywords

• Equivalent theorem
• Approximation
• Orlicz space
• Linear combination
• K-functional
• Weighted Jacobi–Baskakov–Kantorovich operator