Approximation for a generalization of Bernstein operators

Abstract

Abstract In this paper, we give a direct approximation theorem, inverse theorem, and equivalent theorem for a generalization of Bernstein operators in the space L p [ 0 , 1 ] $L_{p}[0,1]$ ( 1 ≤ p ≤ ∞ $1\leq p \leq\infty$ ).

Keywords

• generalized Bernstein-Kantorovich operators
• modulus of smoothness
• K-functional
• equivalent approximation theorem