{"title":"Riemann-Liouville分数积分型Szász-Mirakyan-Kantorovich算子的近似性质","authors":"Nazim Mahhmudov, M. Kara","doi":"10.7153/jmi-2022-16-86","DOIUrl":null,"url":null,"abstract":". In the present paper, we introduce the Riemann-Liouville fractional integral type Sz´asz- Mirakyan-Kantorovich operators. We investigate the order of convergence by using Lipschitz-type maximal functions, second order modulus of smoothness and Peetre’s K-functional. Weigh- ted approximation properties of these operators in terms of modulus of continuity have been dis-cussed. Then, Vorononskaja-type type theorem are obtained. Moreover, bivariate the Riemann- Liouville fractional integral type Sz´asz-Mirakyan-Kantorovich operators are constructed. The last section is devoted to graphical representation and numerical results for these operators.","PeriodicalId":49165,"journal":{"name":"Journal of Mathematical Inequalities","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Approximation properties of the Riemann-Liouville fractional integral type Szász-Mirakyan-Kantorovich operators\",\"authors\":\"Nazim Mahhmudov, M. Kara\",\"doi\":\"10.7153/jmi-2022-16-86\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In the present paper, we introduce the Riemann-Liouville fractional integral type Sz´asz- Mirakyan-Kantorovich operators. We investigate the order of convergence by using Lipschitz-type maximal functions, second order modulus of smoothness and Peetre’s K-functional. Weigh- ted approximation properties of these operators in terms of modulus of continuity have been dis-cussed. Then, Vorononskaja-type type theorem are obtained. Moreover, bivariate the Riemann- Liouville fractional integral type Sz´asz-Mirakyan-Kantorovich operators are constructed. The last section is devoted to graphical representation and numerical results for these operators.\",\"PeriodicalId\":49165,\"journal\":{\"name\":\"Journal of Mathematical Inequalities\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Inequalities\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.7153/jmi-2022-16-86\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Inequalities","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/jmi-2022-16-86","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Approximation properties of the Riemann-Liouville fractional integral type Szász-Mirakyan-Kantorovich operators
. In the present paper, we introduce the Riemann-Liouville fractional integral type Sz´asz- Mirakyan-Kantorovich operators. We investigate the order of convergence by using Lipschitz-type maximal functions, second order modulus of smoothness and Peetre’s K-functional. Weigh- ted approximation properties of these operators in terms of modulus of continuity have been dis-cussed. Then, Vorononskaja-type type theorem are obtained. Moreover, bivariate the Riemann- Liouville fractional integral type Sz´asz-Mirakyan-Kantorovich operators are constructed. The last section is devoted to graphical representation and numerical results for these operators.
期刊介绍:
The ''Journal of Mathematical Inequalities'' (''JMI'') presents carefully selected original research articles from all areas of pure and applied mathematics, provided they are concerned with mathematical inequalities and their numerous applications. ''JMI'' will also periodically publish invited survey articles and short notes with interesting results treating the theory of inequalities, as well as relevant book reviews. Only articles written in the English language and in a lucid, expository style will be considered for publication. ''JMI'' primary audience are pure mathematicians, applied mathemathicians and numerical analysts.
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