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Journal of Computational Mathematics 2024年第2期42卷 337-354页

作者： Wansheng Wang Department of Mathematics Shanghai Normal UniversityShanghai 200234China

Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in banach space.To break through the order barrier p≤1 of unconditionally contractive linear multistep methods for dissipative systems,strongly dissipative systems are introduced.By employing the error growth function of the methods,new contractivity and convergence results of stepsize-dependent linear multistep methods on infinite integration intervals are provided for strictly dissipative systems(ω<0)and strongly dissipative systems.Some applications of the main results to several linear multistep methods,including the trapezoidal rule,are supplied.The theoretical results are also illustrated by a set of numerical experiments.

关键词： Nonlinear evolution equation Linear multistep methods ω-dissipative operators Stability Convergence banach space

Some Mean Convergence Theorems for the Maximum of Normed Double Sums of banach space Valued Random Elements

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1727-1740页

作者： Andrew ROSALSKY Lê V?n THàNH Nguyen Thi THUY Department of Statistics University of Florida Department of Mathematics Vinh University High School for Gifted Students Vinh University

In this correspondence, we establish mean convergence theorems for the maximum of normed double sums of banach space valued random elements. Most of the results pertain to random elements which are M-dependent. We expand and improve a number of particular cases in the literature on mean convergence of random elements in banach spaces. One of the main contributions of the paper is to simplify and improve a recent result of Li, Presnell, and Rosalsky [Journal of Mathematical Inequalities, 16, 117–126(2022)]. A new maximal inequality for double sums of M-dependent random elements is proved which may be of independent interest. The sharpness of the results is illustrated by four examples.

关键词： Double sum mean convergence Rademacher type p banach space banach space valued random element M -dependent random elements 60F25 60B11 60B12

Weakly Compact Sets and Riesz Representation Theorem in Musielak Sequence spaces

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Acta Mathematica Sinica,English Series 2024年第2期40卷 467-484页

作者： Wan Zhong GONG Si Yu SHI Zhong Rui SHI Department of Mathematics Anhui Normal UniversityWuhu 241000P.R.China Smeal College of Business Pennsylvania State UniversityUniversity ParkPennsylwania 16802USA Department of Mathematics Shanghai UniversityShanghai 200444P.R.China

In this work,we give some criteria of the weakly compact sets and a representation theorem of Riesz's type in Musielak sequence spaces using the ideas and techniques of sequence spaces and Musielak function.Finally,as an immediate consequence of the criteria considered in this paper,the criteria of the weakly compact sets of Orlicz sequence spaces are deduced.

关键词： Compact set weak topology banach space dual space Musielak sequence spaces

ON A UNIVERSAL INEQUALITY FOR APPROXIMATE PHASE ISOMETRIES

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Acta Mathematica Scientia 2024年第3期44卷 823-838页

作者：戴端旭阙海新孙龙发郑本拓 School of Science Jimei UniversityXiamen361021China Hebei Key Laboratory of Physics and Energy Technology School of Mathematics and PhysicsNorth China Electric Power UniversityBaoding071003China Department of Mathematical Sciences University of MemphisMemphisTN38152USA

Let X and Y be two normed spaces.Let U be a non-principal ultrafilter on N.Let g:X→Y be a standard ε-phase isometry for someε≥ 0,i.e.,g(0)=0,and for all u.v ∈ X,||‖g(u)+g(v)‖±‖g(u)-g(v)‖|-|‖u+v‖±‖u-v‖| |≤ε.The mapping g is said to be a phase isometry provided that ε=0.In this paper,we show the following universal inequality of g:for each u^(*) ∈ w^(*)-exp ‖u^(*)‖B_(x^(*)),there exist a phase function σ_(u^(*)):X→{-1,1} and φ ∈ Y^(*) with ‖φ‖=‖u^(*)‖≡α satisfying that|(u^(*),u)-σ_(u^(*))(u))|≤5/2εα,for all u ∈ X.In particular,let X be a smooth banach space.Then we show the following:(1) the universal inequality holds for all u^(*) ∈ X^(*);(2) the constant 5/2 can be reduced to 3/2 provided that Y~*is strictly convex;(3) the existence of such a g implies the existence of a phase isometryΘ:X→Y such that■ provided that Y^(**) has the w^(*)-Kadec-Klee property(for example,Y is both reflexive and locally uniformly convex).

关键词： ε-phase isometry phase isometry banach space

A Nonclassical LIL for Geometrically Weighted Series in banach space

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Acta Mathematica Sinica,English Series 2013年第7期29卷 1413-1420页

作者： Ke Ang FU Xiao Rong YANG Wei HUANG School of Statistics and Mathematics Zhejiang Gongshang University Department of Mathematics Zhejiang University

We consider efficient methods for the recovery of block sparse signals from underdetermined system of linear equations. We show that if the measurement matrix satisfies the block RIP with δ2s 〈 0.4931, then every block s-sparse signal can be recovered through the proposed mixed l2/ll-minimization approach in the noiseless case and is stably recovered in the presence of noise and mismodeling error. This improves the result of Eldar and Mishali （in IEEE Trans. Inform. Theory 55： 5302-5316, 2009）. We also give another sufficient condition on block RIP for such recovery method： 58 〈 0.307.

关键词： banach space geometrically weighted series nonclassical law of the iterated logarithm

ITERATIVE SOLUTIONS FOR SYSTEMS OF NONLINEAR OPERATOR EQUATIONS IN banach space

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Acta Mathematica Scientia 2003年第4期23卷 461-466页

作者：宋光兴 Department of Mathematics University of Petroleum Dongying 257061 China

By using partial order method, the existence, uniqueness and iterative approximation of solutions for a class of systems of nonlinear operator equations in banach space are discussed. The results obtained in this pape... 详细信息

关键词： System of operator equations solution iterative technique cone and partial ordering banach space

On Hyperinvariant Subspaces of Contraction Operators on a banach space Whose Spectrum Contains the Unit Circle

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Acta Mathematica Sinica,English Series 2008年第9期24卷 1471-1474页

作者： Ming Xue LIU Department of Mathematics Guangdong Polytechnic Normal University Guangzhou 510665 P. R. China Department of Mathematics Guangdong Polytechnic Normal University Guangzhou P. R. China

In this paper, we prove that every operator in a class of contraction operators on a banach space whose spectrum contains the unit circle has a nontrivial hyperinvariant subspace.

关键词： banach space contraction operator invariant subspace

Every Weakly Compact Set Can Be Uniformly Embedded into a Reflexive banach space

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Acta Mathematica Sinica,English Series 2009年第7期25卷 1109-1112页

作者： Li Xin CHENG Qing Jin CHENG Zheng Hua LUO Wen ZHANG Department of Mathematics Xiamen University Xiamen 361005 P. R. China

Based on an application of the Davis-Figiel-Johnson-Pelzyski procedure, this note shows that every weakly compact subset of a banach space can be uniformly embedded into a reflexive banach space. As its application, we present the recent renorming theorems for reflexive spaces of Odell- Schlumprecht and Hajek-Johanis can be extended and localized to weakly compact convex subsets of an arbitrary banach space.

关键词： banach space weakly compact set renorming

KNESER＇S　THEOREM　FOR　NONLINEAR　INTEGRO－DIFFERENTIAL　EQUATIONS　OF　VOLTERRA　TYPE　IN　A　banach　space

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Acta Mathematica Scientia 1996年第S1期16卷 15-21页

作者：范进军 Department of Mathematics Shandong Normal University Jinan 250014 China

In this paper. we consider the following Cauchy problem of first order nonlinear integro-differential equation of Volterra typebeing real banach space.The problem (1) is equivalent to the following equationWe study the toplogical properties of the problenl (3)-continuum. The obtained result is the extention of the results of the ordinary differential equation and the reference [1].

关键词： banach space Measures of noncompact

Incompleteness of Complex Exponential System in banach space

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Northeastern Mathematical Journal 2004年第3期20卷 303-308页

作者：邓冠铁 Department of Mathematics Beijing Normal University Beijing 100875n this paper we obtain a necessary and sufficient condition for the incompleteness of complex exponential system in Cα where Cαis a weighted Banach space of complex continuous functions f on the real axis R with f(t) exp{-α(t)} vanishing at infinity in the uniform norm.

In this paper, we obtain a necessary and sufficient condition for the incompleteness of complex exponential system in Cα, where Cα is a weighted banach space of complex continuous functions f on the real axis R with... 详细信息

关键词： incompleteness banach space exponential system