{"title":"On Banaś modulus of smoothness and Gao Pythagorean constant of Lp(μ)","authors":"Alireza Amini-Harandi, Malihe Peyvaste","doi":"10.1016/j.jmaa.2024.129046","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we first compute the Banaś modulus of smoothness of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>, which gives a solution to the problem posed by Banaś in 1986 (see Problem 4 of Banas (1986) <span><span>[1]</span></span>). Then, we introduce and calculate Gao Pythagorean constant of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>μ</mi><mo>)</mo></math></span>, which extends and improves some main results of Gao (2006) <span><span>[3]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 129046"},"PeriodicalIF":1.2000,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24009685","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper, we first compute the Banaś modulus of smoothness of , which gives a solution to the problem posed by Banaś in 1986 (see Problem 4 of Banas (1986) [1]). Then, we introduce and calculate Gao Pythagorean constant of , which extends and improves some main results of Gao (2006) [3].
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The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
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