共查询到20条相似文献,搜索用时 265 毫秒
1.
Guo-Liang Xu & Guo-Zhong Zhuang 《计算数学(英文版)》1993,11(3):225-235
This paper provides a new method for approximating matrix-valued functions — square Padéapproximation. Some computational methods of the approximants are given. For accelerating matrix sequences, a family of nonlinear extrapolation formulas based on the square Padé approximation is given, a convergence acceleration theorem is proved and numerical examples are presented. 相似文献
2.
本文建立了拟模Abelian群上双参数算子族逼近的外推定理,所得的结果包含了DeVoreR.等人对正规逼近族之最佳逼近所建立的外推定理,且所需的条件更弱.同时从本文的结果立即可以建立起算子逼近的外推定理. 相似文献
3.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(6):2620-2627
A nonlinear finite difference scheme is studied for solving the Kuramoto–Tsuzuki equation. Because the maximum estimate of the numerical solution can not be obtained directly, it is difficult to prove the stability and convergence of the scheme. In this paper, we introduce the Brouwer-type fixed point theorem and induction argument to prove the unique existence and convergence of the nonlinear scheme. An iterative algorithm is proposed for solving the nonlinear scheme, and its convergence is proved. Based on the iterative algorithm, some linearized schemes are presented. Numerical examples are carried out to verify the correction of the theory analysis. The extrapolation technique is applied to improve the accuracy of the schemes, and some interesting results are obtained. 相似文献
4.
Dong Liang Guanying SunWenqia Wang 《Journal of Computational and Applied Mathematics》2011,235(13):3841-3858
In this paper, we analyze two new second-order characteristic schemes in time and age for an age-structured population model with nonlinear diffusion and reaction. By using the characteristic difference to approximate the transport term and the average along the characteristics to treat the nonlinear spatial diffusion and reaction terms, an implicit second-order characteristic scheme is proposed. To compute the nonlinear approximation system, an explicit second-order characteristic scheme in time and age is further proposed by using the extrapolation technique. The global existence and uniqueness of the solution of the nonlinear approximation scheme are established by using the theory of variation methods, Schauder’s fixed point theorem, and the technique of prior estimates. The optimal error estimates of second order in time and age are strictly proved for both the implicit and the explicit characteristic schemes. Numerical examples are given to illustrate the performance of the methods. 相似文献
5.
We prove an extrapolation theorem for the nonlinear m-term approximation with respect to a system of functions satisfying very mild conditions. This theorem allows us to prove endpoint Lp-Lq estimates in nonlinear approximation. As a consequence, some known endpoint estimates can be deduced directly and some new estimates are also obtained. Finally, applications of these new estimates are given to spherical m-widths and m-term approximation of the weighted Besov classes. 相似文献
6.
Odysseas Bakas 《Archiv der Mathematik》2019,113(5):537-549
In this note, a variant of Yano’s classical extrapolation theorem for sublinear operators acting on analytic Hardy spaces over the torus is obtained. 相似文献
7.
V.M. Kokilashvili 《Journal of Mathematical Analysis and Applications》2009,352(1):15-34
Last years there was increasing an interest to the so-called function spaces with non-standard growth, known also as variable exponent Lebesgue spaces. For weighted such spaces on homogeneous spaces, we develop a certain variant of Rubio de Francia's extrapolation theorem. This extrapolation theorem is applied to obtain the boundedness in such spaces of various operators of harmonic analysis, such as maximal and singular operators, potential operators, Fourier multipliers, dominants of partial sums of trigonometric Fourier series and others, in weighted Lebesgue spaces with variable exponent. There are also given their vector-valued analogues. 相似文献
8.
Paul-Emile Maingé 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):720-1252
This paper deals with a general fixed point method which unifies relaxation factors and a two step inertial type extrapolation. These strategies are intended to improve the convergence of many existing algorithms. A convergence theorem, which improves the known ones, is established in this new setting. 相似文献
9.
Fixed point theorems and convergence theorems for generalized nonspreading mappings in Banach spaces
Wataru Takahashi Ngai-Ching Wong Jen-Chih Yao 《Journal of Fixed Point Theory and Applications》2012,11(1):159-183
In this paper, we first prove a general fixed point theorem for nonlinear mappings in a Banach space. Then we prove a nonlinear mean convergence theorem of Baillon??s type and a weak convergence theorem of Mann??s type for 2-generalized nonspreading mappings in a Banach space. 相似文献
10.
11.
Javier Duoandikoetxea 《Journal of Functional Analysis》2011,260(6):1886-1901
We use an appropriate factorization of the Ap weights to give another proof of the extrapolation theorem of Rubio de Francia. It provides sharp bounds in terms of the Ap-constant of the weights. Then we extend the result to more general settings including off-diagonal and partial range extrapolation. Among the applications, we prove by iteration a multivariable extrapolation theorem and give a sharp bound for Calderón-Zygmund operators on Lp(w) for weights in Aq (q<p). 相似文献
12.
A method for the numerical solution of linear Volterra integro-differentialequations of the first kind is obtained through the use of simplequadrature rules. A convergence theorem and asymptotic errorestimates are derived. The error estimates are used to justifythe application of Richardson's extrapolation. In this way oneobtains a simple method whose order of convergence is four. 相似文献
13.
Watcharaporn Cholamjiak Prasit Cholamjiak Suthep Suantai 《Journal of Fixed Point Theory and Applications》2018,20(1):42
In this work, our interest is in investigating the monotone inclusion problems in the framework of real Hilbert spaces. For solving this problem, we propose an inertial forward–backward splitting algorithm involving an extrapolation factor. We then prove its strong convergence under some mild conditions. Finally, we provide some applications including the numerical experiments for supporting our main theorem. 相似文献
14.
《数学季刊》2014,(4)
In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green's function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii's fixed point theorem. 相似文献
15.
Comparison theorem and uniqueness of positive solutions for sublinear elliptic equations 总被引:1,自引:0,他引:1
Ryuji Kajikiya 《Archiv der Mathematik》2008,91(5):427-435
In semilinear elliptic equations, we prove that the necessary and sufficient condition for the comparison theorem of positive
solutions to be valid is that the nonlinear term is sublinear. Our theorem needs neither any regularity of the nonlinear term
nor the smoothness of the boundary. Applying this theorem, we prove the uniqueness of positive solutions for the Dirichlet
problem.
Received: 9 April 2008 相似文献
16.
In this paper, we reveal several basic properties about nonlinear vector-valued weighted pseudo almost automorphic functions, including equivalence, completeness, translation invariance, composition theorem, and convolution theorem of these functions. We also give some concrete examples to illustrate our results. Finally, we obtain a new existence theorem of nonlinear weighted pseudo almost automorphic solutions for semilinear evolution equations in Banach spaces. 相似文献
17.
Cemil Tunç 《Journal of the Egyptian Mathematical Society》2012,20(1):43-45
The aim of this paper is to establish an instability theorem for a certain sixth order nonlinear delay differential equation. The proof of the theorem is based on the use of Lyapunov–Krasovskii functional approach. By this work, we improve an instability result obtained in the literature for a certain sixth order nonlinear differential equation without delay to the instability of the zero solution of a certain sixth order nonlinear delay differential equation. 相似文献
18.
In this paper, we prove some coupled coincidence point theorems for such nonlinear contraction mappings having a mixed monotone property in partially ordered metric spaces by dropping the condition of commutative. We also prove coupled common fixed point theorem for w-compatible mappings. An example of a nonlinear contraction mapping which is not applied by Lakshmikantham and ?iri?’s theorem [1] but applied by our result is given. Further, we apply our results to the existence theorem for solution of nonlinear integral equations. 相似文献
19.
Journal of Fourier Analysis and Applications - We give an extension of Rubio de Francia’s extrapolation theorem for functions taking values in $${{\,\mathrm{UMD}\,}}$$ Banach function spaces... 相似文献
20.
在[1]中我们已证明了一个一般的随机不动点定理并给出了某些应用,在本文中我们将给出该结果的进一步应用.首先证明了一随机Darbo不动点定理,然后利用此定理在紧性假设下给出了非线性随机Volterra积分方程和非线性随机微分方程Cauchy问题随机解的存在性准则.我们的定理改进和推广了Lakshmikantham[3,4],Vaugham[2],De Blasi和Myjak[5]等人的结果. 相似文献