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Constructive Mathematical Analysis最新文献

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Decay of Fourier transforms and generalized Besov spaces 傅里叶变换的衰变与广义Besov空间
Constructive Mathematical Analysis Pub Date : 2019-07-23 DOI: 10.33205/cma.646557
T. Jordão
{"title":"Decay of Fourier transforms and generalized Besov spaces","authors":"T. Jordão","doi":"10.33205/cma.646557","DOIUrl":"https://doi.org/10.33205/cma.646557","url":null,"abstract":"A characterization of the generalized Lipschitz and Besov spaces in terms of decay of Fourier transforms is given. In particular, necessary and sufficient conditions of Titchmarsh type are obtained. The method is based on two-sided estimate for the rate of approximation of a $beta$-admissible family of multipliers operators in terms of decay properties of Fourier transform.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42621698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On Some Bivariate Gauss-Weierstrass Operators 关于一些二元高斯-魏尔斯特拉斯算子
Constructive Mathematical Analysis Pub Date : 2019-06-01 DOI: 10.33205/CMA.518582
G. Krech, Ireneusz Krech
{"title":"On Some Bivariate Gauss-Weierstrass Operators","authors":"G. Krech, Ireneusz Krech","doi":"10.33205/CMA.518582","DOIUrl":"https://doi.org/10.33205/CMA.518582","url":null,"abstract":"The aim of the paper is to investigate the approximation properties of bivariate generalization of Gauss-Weierstrass operators associated with the Riemann-Liouville operator. In particular, the approximation error will be estimated by these operators in the space of functions defined and continuous in the half-plane $(0, infty) times mathbb{R}$, and bounded by certain exponential functions.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46087339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
A General Korovkin Result Under Generalized Convergence 广义收敛下的一般Korovkin结果
Constructive Mathematical Analysis Pub Date : 2019-06-01 DOI: 10.33205/CMA.530987
P. Garrancho
{"title":"A General Korovkin Result Under Generalized Convergence","authors":"P. Garrancho","doi":"10.33205/CMA.530987","DOIUrl":"https://doi.org/10.33205/CMA.530987","url":null,"abstract":"In this paper the classic result of Korovkin about the convergence of sequences of functions defined from sequences of linear operators is reformulated in terms of generalized convergence. This convergence extends some others given in the literature. The operator of the sequence fulfill a shape preserving property more general than the positivity. This property is related with certain extension of the notion of derivative. This extended derivative is precisely the object of the approximation process. The study is completed by analysing the conditions for the existence of an asymptotic formula, from which some interesting consequences are derived as a local version of the shape preserving property. Finally, as applications of the previous results, the author use the following notion of generalized convergence, an extension of Norlund-Cesaro summability given by V. Loku and N. L. Braha in 2017. A way to transfer a notion of generalized convergence to approximation theory by means of linear operators is showed .","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47439329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Set-Valued Additive Functional Equations 集值可加函数方程
Constructive Mathematical Analysis Pub Date : 2019-06-01 DOI: 10.33205/CMA.528182
Choonkill Park, Sungsik Yun, Jung Rye Lee, D. Shin
{"title":"Set-Valued Additive Functional Equations","authors":"Choonkill Park, Sungsik Yun, Jung Rye Lee, D. Shin","doi":"10.33205/CMA.528182","DOIUrl":"https://doi.org/10.33205/CMA.528182","url":null,"abstract":"In this paper, we  introduce  set-valued additive  functional equations and prove the Hyers-Ulam stability of the  set-valued additive  functional equations by using the fixed point method.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46008169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On Geometric Series of Positive Linear Operators 关于线性正算子的几何级数
Constructive Mathematical Analysis Pub Date : 2019-06-01 DOI: 10.33205/CMA.506015
R. Păltănea
{"title":"On Geometric Series of Positive Linear Operators","authors":"R. Păltănea","doi":"10.33205/CMA.506015","DOIUrl":"https://doi.org/10.33205/CMA.506015","url":null,"abstract":"We study the existence and the norm of operators obtained as power series of linear positive operators with particularization to Bernstein operators. We also obtain a Voronovskaja-kind theorem.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45720386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
General Multivariate Iyengar Type Inequalities 一般多元Iyengar型不等式
Constructive Mathematical Analysis Pub Date : 2019-06-01 DOI: 10.33205/CMA.543560
G. Anastassiou
{"title":"General Multivariate Iyengar Type Inequalities","authors":"G. Anastassiou","doi":"10.33205/CMA.543560","DOIUrl":"https://doi.org/10.33205/CMA.543560","url":null,"abstract":"Here we give a variety of general multivariate Iyengar type inequalities for not necessarily radial functions defined on the shell and ball. Our approach is based on the polar coordinates in $mathbb{R}^{N}$, $Ngeq 2$, and the related multivariate polar integration formula. Via this method we transfer well-known univariate Iyengar type inequalities and univariate author's related results into general multivariate Iyengar inequalities.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41957537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Quantitative Estimates for $L^p$-Approximation by Bernstein-Kantorovich-Choquet Polynomials with Respect to Distorted Lebesgue Measures Bernstein-Kantorovich-Choquet多项式关于变形Lebesgue测度的$L^p$-逼近的定量估计
Constructive Mathematical Analysis Pub Date : 2019-03-01 DOI: 10.33205/CMA.481186
S. Gal, S. Trifa
{"title":"Quantitative Estimates for $L^p$-Approximation by Bernstein-Kantorovich-Choquet Polynomials with Respect to Distorted Lebesgue Measures","authors":"S. Gal, S. Trifa","doi":"10.33205/CMA.481186","DOIUrl":"https://doi.org/10.33205/CMA.481186","url":null,"abstract":"For the univariate Bernstein-Kantorovich-Choquet polynomials written in terms of the Choquet integral with respect to a distorted probability Lebesgue measure, we obtain quantitative approximation estimates for the $L^{p}$-norm, $1le p<+infty$, in terms of a $K$-functional.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45570018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Some Prev{s}i'{c} Type Results in $b-$Dislocated Metric Spaces 某些Prev{s}i'{c}类型在$b-$Dislocated度量空间中的结果
Constructive Mathematical Analysis Pub Date : 2019-03-01 DOI: 10.33205/CMA.499171
A. Babu, T. Došenović, M. Ali, S. Radenović, K. Rao
{"title":"Some Prev{s}i'{c} Type Results in $b-$Dislocated Metric Spaces","authors":"A. Babu, T. Došenović, M. Ali, S. Radenović, K. Rao","doi":"10.33205/CMA.499171","DOIUrl":"https://doi.org/10.33205/CMA.499171","url":null,"abstract":"In this paper, we obtain a Prev{s}i'{c} type common fixed point theorem for four maps in $b$-dislocated metric spaces. We also present one example to illustrate our main theorem. Further, we obtain two more corollaries.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42369463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
A Quantitative Estimate for the Sampling Kantorovich Series in Terms of the Modulus of Continuity in Orlicz Spaces 基于Orlicz空间连续模的抽样Kantorovich级数的定量估计
Constructive Mathematical Analysis Pub Date : 2019-03-01 DOI: 10.33205/CMA.484500
D. Costarelli, G. Vinti
{"title":"A Quantitative Estimate for the Sampling Kantorovich Series in Terms of the Modulus of Continuity in Orlicz Spaces","authors":"D. Costarelli, G. Vinti","doi":"10.33205/CMA.484500","DOIUrl":"https://doi.org/10.33205/CMA.484500","url":null,"abstract":"In the present paper we establish a quantitative estimate for the sampling Kantorovich operators with respect to the modulus of continuity in Orlicz spaces defined in terms of the modular functional. At the end of the paper, concrete examples are discussed, both for what concerns the kernels of the above operators, as well as for some concrete instances of Orlicz spaces.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44484958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 23
A Note on the Differences of Two Positive Linear Operators 关于两个线性正算子差的一个注记
Constructive Mathematical Analysis Pub Date : 2019-03-01 DOI: 10.33205/CMA.469114
Vijay Gupta, G. Tachev
{"title":"A Note on the Differences of Two Positive Linear Operators","authors":"Vijay Gupta, G. Tachev","doi":"10.33205/CMA.469114","DOIUrl":"https://doi.org/10.33205/CMA.469114","url":null,"abstract":"In the present note we find the general estimate in terms of Paltanea's modulus of continuity. In the end, we consider some examples and we apply our result for such examples to obtain the quantitative estimates for the difference of operators.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44779012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
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