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.
Highlights
Introduction and Main ResultsThroughout this paper, we use C to denote an absolute constant independent of anything, which may be not necessarily the same in different cases.There are many types of integral operators
In the paper [8], Ueki provided a characterization for the boundedness and compactness of the Li-SteviÄ type integral operators g
We investigate the approximation of linear combinations of modified summation operators of integral type Bn ( f, x ) in Orlicz spaces LâΊ [0, â)
Summary
Throughout this paper, we use C to denote an absolute constant independent of anything, which may be not necessarily the same in different cases. For f â LâΊ [0, â), the modified summation operators of integral type Bn ( f , x ) are defined in [16] as. Han and Wu [16] obtained the following direct, inverse, and equivalent theorems of modified summation operators of integral type in Orlicz spaces. Between the weighted modulus of smoothness and the modified weighted K-functional, there exists the following equivalent theorem. Between the weighted modulus of smoothness and the weighted K-functional, there exists the following equivalent theorem. There are few results about linear combinations of modified summation operators of integral type Bn ( f , x ). We investigate the approximation of linear combinations of modified summation operators of integral type Bn ( f , x ) in Orlicz spaces LâΊ [0, â). These main results improve some conclusions in [19] and increase the approximating speed of corresponding operators
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