On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces

Abstract

In this paper, the authors introduce the Orlicz spaces 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 combinations of modified summation operators of integral type in the Orlicz spaces.

Keywords

• approximation
• linear combination
• direct theorem
• inverse theorem
• equivalent theorem
• Orlicz space
• modified summation operators of integral type
• K-functional
• modulus