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Generalized $g$-iterated fractional approximations by sublinear operators 次线性算子的广义$g$迭代分数近似
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/am2400-1-2020
G. Anastassiou
{"title":"Generalized $g$-iterated fractional approximations by sublinear operators","authors":"G. Anastassiou","doi":"10.4064/am2400-1-2020","DOIUrl":"https://doi.org/10.4064/am2400-1-2020","url":null,"abstract":". We study approximation of functions by sublinear positive operators with applications to several max-product operators under generalized g -iterated fractional differentiability. Our work is based on our generalized g -iterated fractional results about positive sublinear operators. We produce Jackson type inequalities under iterated initial conditions. Our approach is quantitative by deriving inequalities with right hand sides involving the modulus of continuity of a generalized g -iterated fractional derivative of the function being approximated.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87900825","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: 2
Highly efficient solvers for nonlinear equations in Banach space Banach空间中非线性方程的高效求解器
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/am2392-1-2020
I. Argyros, S. George
{"title":"Highly efficient solvers for nonlinear equations in Banach space","authors":"I. Argyros, S. George","doi":"10.4064/am2392-1-2020","DOIUrl":"https://doi.org/10.4064/am2392-1-2020","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88184005","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: 0
On the eigenvalues and eigenfunctions for a free boundary problem for incompressible viscous magnetohydrodynamics 不可压缩粘性磁流体力学自由边界问题的特征值和特征函数
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/AM2358-10-2018
P. Kacprzyk, W. Zaja̧czkowski
{"title":"On the eigenvalues and eigenfunctions for a free boundary problem for incompressible viscous magnetohydrodynamics","authors":"P. Kacprzyk, W. Zaja̧czkowski","doi":"10.4064/AM2358-10-2018","DOIUrl":"https://doi.org/10.4064/AM2358-10-2018","url":null,"abstract":"The motion of incompressible magnetohydrodynamics (mhd) in a domain bounded by a free surface and coupled through it with an external electromagnetic field is considered. Transmission conditions for electric currents and magnetic fields are prescribed on the free surface. In this paper we show the idea of the proof of local existence by the method of successive approximations. For this we need linearized problems: the Stokes system for the velocity and pressure and the linear transmission problem for the electromagnetic field. We do not prove the local existence of solutions to the original problem but we show existence of a fundamental basis of functions for the linearized problems. Once we have such a basis, the existence of solutions to the linear problems can be shown by the Faedo–Galerkin method, as in other papers of Kacprzyk. The existence of solutions of the linear systems can also be shown by the method of regularizer.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89280880","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: 0
Extensions of Kantorovich-type theorems for Newton’s method 牛顿方法中kantorovich型定理的扩展
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/am2352-1-2018
I. Argyros, S. George, D. R. Sahu
{"title":"Extensions of Kantorovich-type theorems for Newton’s method","authors":"I. Argyros, S. George, D. R. Sahu","doi":"10.4064/am2352-1-2018","DOIUrl":"https://doi.org/10.4064/am2352-1-2018","url":null,"abstract":". We extend the applicability of Newton’s method, so we can approximate a locally unique solution of a nonlinear equation in a Banach space setting in cases not covered before. To achieve this, we find a more precise set containing the Newton iterates than in earlier works.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74683046","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: 0
The optimal time decay rates for incompressible viscoelastic fluids in critical framework 临界框架下不可压缩粘弹性流体的最佳时间衰减率
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/am2409-5-2020
Dandan Ding, Meiling Chi, Fuyi Xu
{"title":"The optimal time decay rates for incompressible viscoelastic fluids in critical framework","authors":"Dandan Ding, Meiling Chi, Fuyi Xu","doi":"10.4064/am2409-5-2020","DOIUrl":"https://doi.org/10.4064/am2409-5-2020","url":null,"abstract":". We study the Cauchy problem for multi-dimensional incompressible viscoelastic fluids in the whole space. The optimal time decay rates of strong solution constructed by Qian (2010), and Zhang (2011) in L 2 critical regularity framework are obtained for low frequencies of the data under a suitable additional condition. The proof relies on an application of Fourier analysis to a mixed parabolic-hyperbolic system, and on a refined time-weighted energy functional. As a by-product, time decay rates of L q - L r type are also captured in the critical framework.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79521635","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: 0
Ball convergence for a sixth-order multi-point method in Banach spaces under weak conditions 弱条件下Banach空间中六阶多点方法的球收敛性
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/AM2350-2-2018
I. Argyros, S. George
{"title":"Ball convergence for a sixth-order multi-point method in Banach spaces under weak conditions","authors":"I. Argyros, S. George","doi":"10.4064/AM2350-2-2018","DOIUrl":"https://doi.org/10.4064/AM2350-2-2018","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"49 1","pages":"133-144"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73105198","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: 0
Adaptive control of diffusion processes with a discounted reward criterion 基于折扣奖励准则的扩散过程自适应控制
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/am2421-10-2020
B. Escobedo-Trujillo, O. Hernández-Lerma, F. A. Alaffita-Hernández
{"title":"Adaptive control of diffusion processes with a discounted reward criterion","authors":"B. Escobedo-Trujillo, O. Hernández-Lerma, F. A. Alaffita-Hernández","doi":"10.4064/am2421-10-2020","DOIUrl":"https://doi.org/10.4064/am2421-10-2020","url":null,"abstract":". The optimal control problem we are dealing with in this paper is to determine control policies that maximize a discounted reward criterion when the dynamic system evolves as a stochastic differential equation (SDE). Both the instantaneous reward function and the SDE’s drift coef-ficient may depend on an unknown parameter. We give conditions ensur-ing the existence of an asymptotically optimal policy using the so-called Principle of Estimation and Control. We illustrate our results with several examples.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78206633","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: 0
Local convergence for multistep high order methods under weak conditions 弱条件下多步高阶方法的局部收敛性
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/am2374-1-2019
I. Argyros, R. Behl, D. González, S. Motsa
{"title":"Local convergence for multistep high order methods under weak conditions","authors":"I. Argyros, R. Behl, D. González, S. Motsa","doi":"10.4064/am2374-1-2019","DOIUrl":"https://doi.org/10.4064/am2374-1-2019","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91235981","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: 1
New Weierstrass elliptic wave solutions of the Davey–Stewartson equation with power law nonlinearity 具有幂律非线性的Davey-Stewartson方程的新weerstrass椭圆波解
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/am2386-4-2020
A. Achab
{"title":"New Weierstrass elliptic wave solutions of the Davey–Stewartson equation with power law nonlinearity","authors":"A. Achab","doi":"10.4064/am2386-4-2020","DOIUrl":"https://doi.org/10.4064/am2386-4-2020","url":null,"abstract":"","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88617560","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: 0
Stochastic approximation procedure in semi-Markov environment applied to alcohol consumption model 半马尔可夫环境下随机逼近法在酒精消费模型中的应用
Applicationes Mathematicae Pub Date : 2020-01-01 DOI: 10.4064/am2382-9-2019
W. Rosa
{"title":"Stochastic approximation procedure in semi-Markov environment applied to alcohol consumption model","authors":"W. Rosa","doi":"10.4064/am2382-9-2019","DOIUrl":"https://doi.org/10.4064/am2382-9-2019","url":null,"abstract":". In this paper, we consider a stochastic approximation procedure with semi-Markov switchings in an averaging scheme with a small parameter.","PeriodicalId":52313,"journal":{"name":"Applicationes Mathematicae","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86879548","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: 0
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