This paper deals with the variation detracting property and rate of approximation of the Chlodovsky type Durrmeyer polynomials in the space of functions of bounded variation with respect to the variation seminorm.
{"title":"On convergence of Chlodovsky type Durrmeyer polynomials in variation seminorm","authors":"Özlem Öksüzer Yılık, H. Karsli, F. Taşdelen","doi":"10.33993/jnaat471-1126","DOIUrl":"https://doi.org/10.33993/jnaat471-1126","url":null,"abstract":"This paper deals with the variation detracting property and rate of approximation of the Chlodovsky type Durrmeyer polynomials in the space of functions of bounded variation with respect to the variation seminorm.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121505576","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}
Using the Fourier series as a projection in the Galerkin method, we approach the solution of the Cauchy singular integral equation. This study is carried in (L^2). Numerical examples are developped to show the effectiveness of this method.
{"title":"Fourier series approximation for the Cauchy singular integral equation","authors":"Hamid Boulares, H. Guebbai, A. Arbaoui","doi":"10.33993/jnaat471-1127","DOIUrl":"https://doi.org/10.33993/jnaat471-1127","url":null,"abstract":"Using the Fourier series as a projection in the Galerkin method, we approach the solution of the Cauchy singular integral equation. This study is carried in (L^2). Numerical examples are developped to show the effectiveness of this method.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130116321","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}
We present a semi-local convergence analysis for a class of iterative methods under generalized conditions. Some applications are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type.
{"title":"Semi-local convergence of iterative methods and Banach space valued functions in abstract fractional calculus","authors":"I. Argyros, G. Anastassiou","doi":"10.33993/jnaat471-1120","DOIUrl":"https://doi.org/10.33993/jnaat471-1120","url":null,"abstract":"We present a semi-local convergence analysis for a class of iterative methods under generalized conditions. Some applications are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127740905","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}
The generalized order of growth and generalized type of an entire function (F^{alpha,beta}) (generalized biaxisymmetric potentials) have been obtained in terms of the sequence (E_n^p(F^{alpha,beta},Sigma_r^{alpha,beta})) of best real biaxially symmetric harmonic polynomial approximation on open hyper sphere (Sigma_r^{alpha,beta}). Moreover, the results of McCoy [8] have been extended for the cases of fast growth as well as slow growth.
{"title":"(L^p)-approximation and generalized growth of generalized biaxially symmetric potentials on hyper sphere","authors":"Devendra Kumar","doi":"10.33993/jnaat471-1109","DOIUrl":"https://doi.org/10.33993/jnaat471-1109","url":null,"abstract":"The generalized order of growth and generalized type of an entire function (F^{alpha,beta}) (generalized biaxisymmetric potentials) have been obtained in terms of the sequence (E_n^p(F^{alpha,beta},Sigma_r^{alpha,beta})) of best real biaxially symmetric harmonic polynomial approximation on open hyper sphere (Sigma_r^{alpha,beta}). Moreover, the results of McCoy [8] have been extended for the cases of fast growth as well as slow growth.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"75 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121014721","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}
A class of transformation is investigated which maps a quadratic integral back to its original form but under a redefinition of free parameters. When this process is iterated, a dynamical system is generated in the form of recursive sequences which involve the parameters of the integrand. The creation of this dynamical system and some of its convergence properties are investigated. MR3724632
{"title":"A class of transformations of a quadratic integral generating dynamical systems","authors":"P. Bracken","doi":"10.33993/jnaat462-1113","DOIUrl":"https://doi.org/10.33993/jnaat462-1113","url":null,"abstract":"A class of transformation is investigated which maps a quadratic integral back to its original form but under a redefinition of free parameters. When this process is iterated, a dynamical system is generated in the form of recursive sequences which involve the parameters of the integrand. \u0000The creation of this dynamical system and some of its convergence properties are investigated. \u0000MR3724632","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128792188","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}
In this paper, we deal with a numerical comparison between two exact simplicial methods for solving a capacitated four-index transportation problem. The first method was developed by R. Zitouni and A. Keraghel for solving this problem [Resolution of a capacitated transportation problem with four subscripts, Kybernetes, Emerald journals, 32, 9/10: 1450-1463 (2003)]. The second approach is the well-known simplex method. We show across some obtained numerical results that the first algorithm competes well with the simplex method.
{"title":"A numerical comparison between two exact simplicial methods for solving a capacitated 4-index transportation problem","authors":"R. Zitouni, M. Achache","doi":"10.33993/jnaat462-1116","DOIUrl":"https://doi.org/10.33993/jnaat462-1116","url":null,"abstract":"In this paper, we deal with a numerical comparison between two exact simplicial methods for solving a capacitated four-index transportation problem. The first method was developed by R. Zitouni and A. Keraghel for solving this problem [Resolution of a capacitated transportation problem with four subscripts, Kybernetes, Emerald journals, 32, 9/10: 1450-1463 (2003)]. The second approach is the well-known simplex method. \u0000We show across some obtained numerical results that the first algorithm competes well with the simplex method.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129789103","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}
Here we study quantitatively the high degree of approximation of sequences of linear operators acting on Banach space valued di§erentiable functions to the unit operator. These operators are bounded by real positive linear companion operators. The Banach spaces considered here are general and no positivity assumption is made on the initial linear operators whose we study their approximation properties. We derive pointwise and uniform estimates which imply the approximation of these operators to the unit assuming di§erentiability of functions. At the end we study the special case where the high order derivative of the on hand function fulÖlls a convexity condition resulting into sharper estimates. MR3724631
{"title":"High order approximation theory for Banach space valued functions","authors":"G. Anastassiou","doi":"10.33993/jnaat462-1112","DOIUrl":"https://doi.org/10.33993/jnaat462-1112","url":null,"abstract":"Here we study quantitatively the high degree of approximation of sequences of linear operators acting on Banach space valued di§erentiable functions to the unit operator. These operators are bounded by real positive linear companion operators. The Banach spaces considered here are general and no positivity assumption is made on the initial linear operators whose we study their approximation properties. We derive pointwise and uniform estimates which imply the approximation of these operators to the unit assuming di§erentiability of functions. At the end we study the special case where the high order derivative of the on hand function fulÖlls a convexity condition resulting into sharper estimates. \u0000MR3724631","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127252021","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}
In this paper, we are concerned about the King-type Baskakov operators defined by means of the preserving functions (e_{0}) and (e^{2ax}, a>0) fixed. Using the modulus of continuity, we show the uniform convergence of new operators to (f). Also, by analyzing the asymptotic behavior of King-type operators with a Voronovskaya-type theorem, we establish shape preserving properties using the generalized convexity.
{"title":"On Baskakov operators preserving the exponential function","authors":"Övgü Gürel Yılmaz, Gupta Vijay, A. Aral","doi":"10.33993/jnaat462-1110","DOIUrl":"https://doi.org/10.33993/jnaat462-1110","url":null,"abstract":"In this paper, we are concerned about the King-type Baskakov operators defined by means of the preserving functions (e_{0}) and (e^{2ax}, a>0) fixed. \u0000Using the modulus of continuity, we show the uniform convergence of new operators to (f). Also, by analyzing the asymptotic behavior of King-type operators with a Voronovskaya-type theorem, we establish shape preserving properties using the generalized convexity.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"359 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128109913","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}
Some Ostrowski-type inequalities are stated for (L_p[u,v]) spaces and for mappings of bounded variations. Applications are also given for obtaining error bounds of some composite quadrature formulae.
{"title":"Some applications of quadrature rules for mappings on (L_p[u,v]) space via Ostrowski-type inequality","authors":"Nazia Irshad, Asif R Khan","doi":"10.33993/jnaat462-1107","DOIUrl":"https://doi.org/10.33993/jnaat462-1107","url":null,"abstract":"Some Ostrowski-type inequalities are stated for (L_p[u,v]) spaces and for mappings of bounded variations. Applications are also given for obtaining error bounds of some composite quadrature formulae.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127155469","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}
In this paper, we present a new accelerating procedure in order to speed up the convergence of Newton-type methods. In particular, we derive iterations with a high and optimal order of convergence. This technique can be applied to any iteration with a low order of convergence. As expected, the convergence of the proposed methods was remarkably fast. The effectiveness of this technique is illustrated by numerical experiments.
{"title":"Accelerating the convergence of Newton-type iterations","authors":"T. Zhanlav, O. Chuluunbaatar, V. Ulziibayar","doi":"10.33993/jnaat462-1105","DOIUrl":"https://doi.org/10.33993/jnaat462-1105","url":null,"abstract":"In this paper, we present a new accelerating procedure in order to speed up the convergence of Newton-type methods. In particular, we derive iterations with a high and optimal order of convergence. This technique can be applied to any iteration with a low order of convergence. \u0000As expected, the convergence of the proposed methods was remarkably fast. The effectiveness of this technique is illustrated by numerical experiments.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134479161","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}
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