On the Mann and Ishikawa iterative approximation of solutions to variational inclusions with accretive type mappings in Banach spaces

The purpose of this paper is to introduce and study the existence of solutions and convergence of Mann and Ishikawa iterative processes for a class of variational inclusions with accretive type mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results by Chang, Ding, Hassouni, Kazmi, Siddiqi, Zeng et al. Foundation item: the National Natural Science Foundation of China (19771058)     

General solution of multi-valued displacement problem of an eccentric circular ring

In this paper, by using N.I, Muskhelishvili’s method a multi-valued displacement problem is considered for an eccentric circular ring. The general expression of stress function is derived in the bipolar coordinate system and its application is explained.     

Interative approximation of fixed points for almost asymptotically nonexpansive type mappings in Banach spaces

IntroductionThroughoutthispaperweassumethatEisarealBanachspace ,E isthedualspaceofE ,DisanonemptysubsetofEandJ:E →2 E isthenormalizeddualitymappingdefinedbyJ(x) =f∈E :〈x ,f〉=‖x‖·‖f‖,‖f‖=‖x‖,　　 x∈E .　　Definition 1　LetT :D →Dbeamapping .1 )Tissaidtobeasymptoticallynonexpansive[1],ifthereexistsasequence kn [1 ,∞)withlimn→∞kn =1suchthat　　　　　‖Tnx-Tny‖≤kn‖x-y‖forall　　x ,y∈D ,n≥0 ;(1 )　　2 )Tissaidtobeofasymptoticallynonexpansivetype[2 ],if　　　　　lims…     

Existence and Approximation of Solutions to Variational Inclusions with Accretive Mappings in Banach Spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒｗｅｓｕｐｐｏｓｅｔｈａｔＸｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅ,Ｘ ｉｓｉｔｓｄｕａｌｓｐａｃｅ ,〈· ,·〉ｉｓｔｈｅｐａｉｒｉｎｇｏｆＸａｎｄＸ .Ｄ(Ｔ)ａｎｄＲ(Ｔ)ｄｅｎｏｔｅｔｈｅｄｏｍａｉｎａｎｄｔｈｅｒａｎｇｅｏｆＴｒｅｓｐｅｃｔｉｖｅｌｙ .ＬｅｔＴ ,Ａ :Ｘ →Ｘ ,ｇ :Ｘ→Ｘ ｂｅｔｈｒｅｅｍａｐｐｉｎｇｓａｎｄφ :Ｘ →Ｒ∪ ∞ ａｐｒｏｐｅｒｃｏｎｖｅｘｌｏｗｅｒｓｅｍｉ＿ｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎ .Ｉｎ 1 999,ｔｈ…     

ON THE ITERATIVE APPROXIMATION PROBLEM OF FIXED POINTS FOR ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒｗｅａｓｓｕｍｅｔｈａｔＥｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅ ,Ｅ ｉｓｔｈｅｄｕａｌｓｐａｃｅｏｆＥ ,ＤｉｓａｎｏｎｅｍｐｔｙｓｕｂｓｅｔｏｆＥａｎｄＪ:Ｅ → 2 Ｅ ｉｓｔｈｅｎｏｒｍａｌｉｚｅｄｄｕａｌｉｔｙｍａｐｐｉｎｇｄｅｆｉｎｅｄｂｙＪ(ｘ) =ｆ∈Ｅ :〈ｘ ,ｆ〉 =‖ｘ‖·‖ｆ‖ ,　‖ｆ‖ =‖ｘ‖ (ｘ∈Ｅ) .　　Ｄｄｆｉｎｉｔｉｏｎ 1 1　ＬｅｔＴ :Ｄ →Ｄｂｅａｍａｐｐｉｎｇ1 )Ｔｉｓｓａｉｄｔｏｂｅａｓｙｍｐｔｏｔｉｃａｌｌｙｎｏ…     

ON THE ITERATIVE APPROXIMATION PROBLEM OF FIXED OINTS FOR ASYMPTOTICALLY NON-EXPANSIVE TYPE MAPPINGS IN BANACH SPACES

Some iterative approximation theorems of fixed points for asymptotically nonexpansive type mappings in Banach spaces are obtained.     

SOLUTIONS OF MAGNETOHYDRODYNAMICS EQUATIONS-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC-PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS (Ⅳ)

This work is the continuation of the discussion of Refs.[1 3].(A) We turn the Magnetohydrodynamics equaitons of isentropic compresible andnon-dissipative magneto-flow into the form of the ideal hydrodynamics equations in thispaper;we can obtain the general Chaplygin equation from Ref.[3],and the generalsduction of this equation.(B)We apply the theory of functions of a complex rariable under Dirac-paulirepresentation,turn the general Magnetohydrodyamics equations of incompressiblemageto-flow into two nonlinear equaitons for flow function and"magneto-flow function",and obtain the exact stable solution of incompressible magnetohydrodynamics equationsunder the condition of stable magnetic field(i.e.under conditon of equality for kinematicalviscid coefficient or viscid diffusion coefficient with magnetic diffusion coefficient).     

CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES

Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi- contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L . B . Ciric , Q . H. Liu , H. E. Rhoades and H. K. Xu , et al. , but also give an affirmative answer to the open question of Rhoades-Naimpally-Singh in convex metric spaces .     

Mann and Ishikawa iterative approximation of solutions form-accretive operator equations

The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m-accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors’ recent results.     

ON REICH''''S OPEN QUESTION

1　IntroductionandPreliminariesThroughoutthispaperweassumethatEisarealBanachspace ,E isthedualspaceofE ,DisanonemptysubsetofEandJ:E → 2 E isthenormalizeddualitymappingdefinedbyJ(x) =f∈E ,　〈x ,f〉 =‖x‖‖f‖ ,　‖x‖ =‖f‖ 　 (x∈E) . (1 )　　Definition 1　LetT :D →Dbeamapping .1 .Tissaidtobeasymptoticallynonexpansive[1],ifthereexistsasequence kn [1 ,∞ )withlimn→∞kn =1suchthat‖Tnx-Tny‖ ≤kn‖x-y‖　forall　x ,y∈D ,n≥ 1 ;　　 2 .Tissaidtobenonexpansive,ifthesequence kn app…     

ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS

The purpose of this paper is to introduce the concept of Φ-pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors’recent results.     

DYNAMICAL EQUATIONS FOR TREESHAPED MULTI-RIGID-BODY SYSTEMS

In this pAper,the“Configuration Graph”for a treeshaped system is brought,whichpresents the position and the arrangement of an arbitrary numberof interconnected rigidbodies.By means of“Configuration Matrix”this paper analyses the motion of treeshapedmulti-rigid-body systems and derives their dynamical equations while it is not necessary tobring out such ideas as“Augmented-Body”and“Subsystem”.In such dynamicalequations,dynamical parameters of a treeshaped multi-rigid-body is closely associatedwith its configuration matrix.     

On a class of generalized nonlinear implicit quasivariational inclusions

ＩｎｔｒｏｄｕｃｔｉｏｎＶａｒｉａｔｉｏｎａｌｉｎｅｑｕａｌｉｔｙｔｈｅｏｒｙａｎｄｃｏｍｐｌｅｍｅｎｔａｒｉｔｙｐｒｏｂｌｅｍｔｈｅｏｒｙｈａｖｅｂｅｃｏｍｅｖｅｒｙｅｆｆｅｃｔｉｖｅａｎｄｐｏｗｅｒｆｕｌｔｏｏｌｓｆｏｒｓｔｕｄｙｉｎｇａｗｉｄｅｒａｎｇｅｏｆｐｒｏｂｌｅｍｓａｒｉｓｉｎｇｉｎｍｅｃｈａｎｉｃｓ,ｍａｔｈｅｍａｔｉｃａｌｐｒｏｇｒａｍｍｉｎｇ,ｏｐｔｉｍｉｚａｔｉｏｎａｎｄｃｏｎｔｒｏｌ,ｅｑｕｉｌｉｂｒｉｕｍｔｈｅｏｒｙｏｆｅｃｏｎｏｍｉｃｓ,ｍａｎａｇｅｍｅｎｔｓｃｉｅｎ…     

ISHIKAWA ITERATIVE PROCESS FOR CONSTRUCTING SOLUTIONS OF m-ACCRETIVE OPERATOR EQUATIONS

1　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＬｅｔＸｂｅａｒｅａｌＢａｎａｃｈｓｐａｃｅｗｉｔｈｔｈｅｎｏｒｍ‖·‖ ,Ｘ ｂｅｔｈｅｄｕａｌｓｐａｃｅｏｆＸ ,ａｎｄ〈· ,·〉ｂｅｔｈｅｇｅｎｅｒａｌｉｚｅｄｄｕａｌｉｔｙｐａｉｒｉｎｇｂｅｔｗｅｅｎＸａｎｄＸ .ＴｈｅｎｏｒｍａｌｉｚｅｄｄｕａｌｉｔｙｍａｐｐｉｎｇＪ:Ｘ →2 Ｘ ｉｓｄｅｆｉｎｅｄｂｙＪ(ｘ) =ｆ∈Ｘ :〈ｘ ,ｆ〉=‖ｘ‖2 =‖ｆ‖2 ,　　ｘ∈Ｘ .　　ＲｅｃａｌｌｔｈａｔｔｈｅｍｏｄｕｌｕｓρＸ( ·)ｏｆｓｍｏｏｔｈｎｅｓｓｏ…     

Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces

A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.     

ON PROBLEM OF NEAREST COMMON FIXED POINT OF NONEXPANSIVE MAPPINGS

The purpose is by using the viscosity approximation method to study the convergence problem of the iterative scheme for an infinite family of nonexpansive mappings and a given contractive mapping in a reflexive Banach space. Under suitable conditions, it was proved that the iterative sequence converges strongly to a common fixed point which was also the unique solution of some variational inequality in a reflexive Banach space. The results presented extend and improve some recent results.     

非光滑动力系统的迭代图胞映射法

分析了图胞映射方法在处理非光滑动力系统过程中遇到的关键问题------胞流扩张. 为了有效减小胞流扩张, 基于迭代图胞映射方法, 通过引入人工顶点集的概念, 构建了非光滑系统迭代图胞映射具体实施方案, 讨论了在此过程中值得注意的事项. 结合典型实例分析, 证实了该方法的有效性.      

UNIFORM NORMAL STRUCTURE AND SOLUTIONS OF REICH’S OPEN QUESTION

The open question raised by Reich is studied in a Banach space with uniform normal structure, whose norm is uniformly Gateaux differentiable. Under more suitable assumptions imposed on an asymptotically nonexpansive mapping, an affirmative answer to Reich＇ s open question is given. The results presented extend and improve Zhang Shisheng＇ s recent ones in the following aspects ： （i） Zhang＇ s stronger condition that the sequence of iterative parameters converges to zero is removed; （ii） Zhang＇ s stronger assumption that the asymptotically nonexpansive mapping has a fixed point is removed; （iii） Zhang＇ s stronger condition that the sequence generated by the Banach Contraction Principle is strongly convergent is also removed. Moreover, these also extend and improve the corresponding ones obtained previously by several authors including Reich, Shioji, Takahashi,Ueda and Wittmann.     

Auxiliary principle and three-step iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities

An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle technique. The convergence of three-step iterative sequences generated by the algorithm is also proved.