{"title":"On the generalized Mellin integral operators","authors":"Cem Topuz, Firat Ozsarac, Ali Aral","doi":"10.1515/dema-2023-0133","DOIUrl":null,"url":null,"abstract":"\n In this study, we give a modification of Mellin convolution-type operators. In this way, we obtain the rate of convergence with the modulus of the continuity of the \n \n \n \n m\n \n m\n \n th-order Mellin derivative of function \n \n \n \n f\n \n f\n \n , but without the derivative of the operator. Then, we express the Taylor formula including Mellin derivatives with integral remainder. Later, a Voronovskaya-type theorem is proved. In the last part, we state order of approximation of the modified operators, and the obtained results are restated for the Mellin-Gauss-Weierstrass operator.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Demonstratio Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/dema-2023-0133","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, we give a modification of Mellin convolution-type operators. In this way, we obtain the rate of convergence with the modulus of the continuity of the
m
m
th-order Mellin derivative of function
f
f
, but without the derivative of the operator. Then, we express the Taylor formula including Mellin derivatives with integral remainder. Later, a Voronovskaya-type theorem is proved. In the last part, we state order of approximation of the modified operators, and the obtained results are restated for the Mellin-Gauss-Weierstrass operator.
在本研究中，我们给出了梅林卷积型算子的一种修正方法。通过这种方法，我们得到了函数 f f 的 m m th 阶梅林导数连续性模数的收敛率，但没有算子的导数。然后，我们用带积分余数的梅林导数来表示泰勒公式。随后，我们证明了沃罗诺夫斯卡娅式定理。在最后一部分，我们说明了修正算子的近似阶数，并对梅林-高斯-韦尔斯特拉斯算子重述了所得结果。
期刊介绍：
Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.
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