On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces
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 operat...
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MDPI AG
2018-12-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/7/1/6 |
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doaj-ad5ec87bd01e40c2acd72f43252ace452020-11-24T23:24:42ZengMDPI AGMathematics2227-73902018-12-0171610.3390/math7010006math7010006On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz SpacesLing-Xiong Han0Feng Qi1College of Mathematics, Inner Mongolia University for Nationalities, Tongliao 028043, Inner Mongolia, ChinaInstitute of Mathematics, Henan Polytechnic University, Jiaozuo 454010, Henan, ChinaIn 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.http://www.mdpi.com/2227-7390/7/1/6approximationlinear combinationdirect theoreminverse theoremequivalent theoremOrlicz spacemodified summation operators of integral typeK-functionalmodulus |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ling-Xiong Han Feng Qi |
| spellingShingle |
Ling-Xiong Han Feng Qi On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces Mathematics approximation linear combination direct theorem inverse theorem equivalent theorem Orlicz space modified summation operators of integral type K-functional modulus |
| author_facet |
Ling-Xiong Han Feng Qi |
| author_sort |
Ling-Xiong Han |
| title |
On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces |
| title_short |
On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces |
| title_full |
On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces |
| title_fullStr |
On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces |
| title_full_unstemmed |
On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces |
| title_sort |
on approximation by linear combinations of modified summation operators of integral type in orlicz spaces |
| publisher |
MDPI AG |
| series |
Mathematics |
| issn |
2227-7390 |
| publishDate |
2018-12-01 |
| description |
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. |
| topic |
approximation linear combination direct theorem inverse theorem equivalent theorem Orlicz space modified summation operators of integral type K-functional modulus |
| url |
http://www.mdpi.com/2227-7390/7/1/6 |
| work_keys_str_mv |
AT lingxionghan onapproximationbylinearcombinationsofmodifiedsummationoperatorsofintegraltypeinorliczspaces AT fengqi onapproximationbylinearcombinationsofmodifiedsummationoperatorsofintegraltypeinorliczspaces |
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1725559395876601856 |