Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space

In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then, we show that the sequence converges strongly to a common element of the two sets. Our results improve and extend the corresponding results reported by many others.

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.

New iterative schemes for strongly relatively nonexpansive mappings and maximal monotone operators

In this paper, some new iterative schemes for approximating the common element of the set of fixed points of strongly relatively nonexpansive mappings and the set of zero points of maximal monotone operators in a real uniformly smooth and uniformly convex Banach space are proposed. Some weak convergence theorems are obtained, which extend and complement some previous work.

g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented, An iterative algorithm for approximating the solutions of generalized implicit wriational- like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved,

Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings

We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108.

Convergence Theorems of Mann and Ishikawa Iterative Processes with Errors for Multivalued Φ-strongly Accretive Mapping

Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160).

利用Monotone Chain算法集成在线地理信息数据生成凸包

介绍了集成Baidu地图API与腾讯地图API,利用腾讯地图的Web服务在线获取特定区域的POI数据,并根据这些数据进行解析得到点群信息,在Internet环境下基于Monotone Chain算法分析点集产生凸包(包围点群最小的凸外壳),并将结果绘制在Web电子地图中,用之作为空间地理信息的挖掘及知识发现作准备。此算法总的时间复杂度是O(n log n)。

SOME RESULTS ON GENERALIZED EQUILIBRIUM PROBLEMS INVOLVING STRICTLY PSEUDOCONTRACTIVE MAPPINGS

In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution set of generalized equilibrium problems and of the fixed point set of strictly pseudocontractive mappings.

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].

CONVERGENCE OF HYBRID VISCOSITY AND STEEPEST-DESCENT METHODS FOR PSEUDOCONTRACTIVE MAPPINGS AND NONLINEAR HAMMERSTEIN EQUATIONS

In this article, we first introduce an iterative method based on the hybrid viscos- ity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping （assuming existence） and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a non- linear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method.

A NEW ALGORITHM FOR MONOTONE INCLUSION PROBLEMS AND FIXED POINTS ON HADAMARD MANIFOLDS WITH APPLICATIONS

In this article,we propose a new algorithm and prove that the sequence generalized by the algorithm converges strongly to a common element of the set of fixed points for a quasi-pseudo-contractive mapping and a demi-contraction mapping and the set of zeros of monotone inclusion problems on Hadamard manifolds.As applications,we use our results to study the minimization problems and equilibrium problems in Hadamard manifolds.

A Monotonicity Condition for Strong Convergence of the Mann Iterative Sequence for Demicontractive Maps in Hilbert Spaces

Let?be a real Hilbert space and?C?be a nonempty closed convex subset of H. Let T : C?→?C?be a demicontractive map satisfying?〈Tx, x〉?≥?‖x‖2 for all?x?∈ D (T). Then the Mann iterative sequence given by?xn + 1?= (1 - an) xn +?anT xn, where an ∈?(0, 1) n?≥?0, converges strongly to an element of F (T):= {x?∈ C : Tx = x}. This strong convergence is obtained without the compactness-type assumptions on C, which many previous results (see e.g. [1]) employed.

Weighted Integral Means of Mixed Areas and Lengths Under Holomorphic Mappings

This note addresses monotonic growths and logarithmic convexities of the weighted （（1-t2）αdt2, -∞〈α〈∞, 0〈t〈1） integral means Aα,β（ f ,·） and Lα,β（ f ,·） of the mixed area （πr2）-βA（ f ,r） and the mixed length （2πr）-βL（ f ,r） （0≤β≤1 and 0〈r〈1） of f （rD） and？f （rD） under a holomorphic map f from the unit disk D into the finite complex plane C.

ITERATIVE APPROXIMATIONS OF φ-HEMICONTRACTIVEMAPPINGS WITHOUT LIPSCHITZ ASSUMPTION

Letq>1,and let E be a real q-uniformly smooth Banach space. Let T: E→E be a continuous φstrongly accretive operator.For a given f E,let x*denote the unique solution of the equation Tx=f.Define the operator H:E→E by Hx=f+x-Tx,and suppose that the range of H is bounded. for any x1 E let {xn}∞n=qin E be the Ishikawa iterative process defined by Under suitable comditions,the Ishikawa iterative process strongly converges to the unique solution of Tx=f.the related result deals with the problems that Ishikawa iterative process strongly converges to the unique fixed point of -hemicontractive mappings.These results generalize results of Osilike [2],Chidume[4,5]and Tan[10],Zeng[11]and several other results from the class of strongly assertive operators and the class of strongly pseudocontractive operators to the much more general class of -trongly accrtive and class of -hemicontractive maps.

Modified Subgradient Extragradient Method for Pseudomonotone Variational Inequalities

Many approaches have been put forward to resolve the variational inequality problem. The subgradient extragradient method is one of the most effective. This paper proposes a modified subgradient extragradient method about classical variational inequality in a real Hilbert interspace. By analyzing the operator’s partial message, the proposed method designs a non-monotonic step length strategy which requires no line search and is independent of the value of Lipschitz constant, and is extended to solve the problem of pseudomonotone variational inequality. Meanwhile, the method requires merely one map value and a projective transformation to the practicable set at every iteration. In addition, without knowing the Lipschitz constant for interrelated mapping, weak convergence is given and R-linear convergence rate is established concerning algorithm. Several numerical results further illustrate that the method is superior to other algorithms.

Some Surjectivity Theorems for Maximal Monotone Operators and Its Application

这份报纸的主要目的是为最大的单调由使用固定的点 theory.We 在反射 Banach 空格印射学习 surjectivity 定理在一些条件下面证明一些是新 surjectivity 定理并且在微分方程给它的申请。

Algorithm for solving a class of general mixed variational inequalities and nonexpansive mappings in Hilbert spaces

This paper is devoted to study the convergence of a new class of generalized system for variational inequalities.The results presented in this paper modify and improve the recent result announced by Chang.[S.S.Chang,H.W.Joseph Lee,Generalzed system for relaxed cocoercive variational inequalities in Hilerbert space,doi:10.1016/j.aml.2006.04.017].

Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings

This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.

THREE-STEP ITERATIONS FOR NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY MONOTONE MAPPINGS

This paper introduces a three-step iteration for finding a common element of the set of fixedpoints of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping by viscosity approximation methods in a Hilbert space.The authors showthat the iterative sequence converges strongly to a common element of the two sets,which solves somevariational inequality.Subsequently,the authors consider the problem of finding a common fixed pointof a nonexpansive mapping and a strictly pseudo-contractive mapping and the problem of finding acommon element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping.The results obtained in this paper extend and improve the correspondingresults announced by Nakajo,Takahashi,and Toyoda.

单调回复关系中稳定的Farey相邻元与拓扑熵

论文旨在利用数论中的Farey相邻元研究高维柱面扭转映射系统的复杂性。鉴于单调回复关系的解和高维柱面扭转映射的轨道之间存在一一对应的关系,问题转化为研究单调回复关系解系统的复杂性。假定单调回复关系的旋转集中有一对稳定的Farey相邻元p/q和p′/q′,利用周期延拓的方法,构造一对交换旋转数p/q和p′/q′的上下解,进而根据Angenent判据,得到系统具有正拓扑熵的结论。