非相容映象的公共不动点定理

本文研究了度量空间中非相容自映象对.利用非相容映象的性质和压缩条件得到一类映象的公共不动点定理,其结果推广了相关文献中的结论.     

构造非线性映射不动点的迭代法

为了构造非线性映射的不动点,许多作者对Mann迭代法进行了研究.后来Ishikawa推广了Mann迭代法,对Hilbert空间H的紧凸子集D的李卜西兹拟压缩映射T,证明了新的迭代法{x_n}强收敛于T的一不动点,{x_n}被定义为     

非扩张映像不动点新的简单逼近算法

提出了一个简单的非扩张映像不动点的逼近算法,该算法通过非迭代的逼近序列来实现.从算法的复杂性来看,提出的算法比经典的Mann迭代算法、Ishikawa迭代算法和Halpern迭代算法更简单.提出的算法紧密联系着非扩张映像不动点的存在性,因此,还得到了非扩张映像的新不动点定理, 拓展和改进了经典的Goebel-Kirk,Kim-Xu等作者的结果.     

Banach空间中非扩张映射不动点的粘性逼近方法

本文研究了非扩张映射不动点的逼近问题的迭代方法.利用粘性逼近方法,在具有一致Gateaux可微范数的Banach空间中,获得了迭代序列的强收敛性,并说明了该序列强收敛于某变分不等式的唯一解.该方法推广了某些文献的结果.     

锥b-度量空间上映射的公共不动点定理

本文研究了锥b-度量空间上四个自映射的公共不动点问题.利用序列逼近的方法,获得了锥b-度量空间上四个自映射的一些公共不动点结果,将锥度量空间中的几个相关结果推广到锥b-度量空间中,并且给出了一个例子以支撑我们的结果.     

模糊度量空间中多变量压缩映射的公共耦合不动点定理

本文提出了多变量映射的一致点的概念.本文的结果是模糊偏序度量空间中不动点定理的一些主要结论从低维到高维的推广.     

VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS

Let H_1, H_2, H_3 be real Hilbert spaces, let A : H_1→ H_3, B : H_2→ H_3 be two bounded linear operators. The split equality common fixed point problem(SECFP) in the infinite-dimensional Hilbert spaces introduced by Moudafi(Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis)is to find x ∈ F(U), y ∈ F(T) such that Ax = By,(1)where U : H_1→ H_1 and T : H_2→ H_2 are two nonlinear operators with nonempty fixed point sets F(U) = {x ∈ H_1: Ux = x} and F(T) = {x ∈ H_2: Tx = x}. Note that,by taking B = I and H_2= H_3 in(1), we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP(1) of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP(1) governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.     

STABILITY OF A PARABOLIC FIXED POINT OF REVERSIBLE MAPPINGS

ＳＴＡＢＩＬＩＴＹＯＦＡＰＡＲＡＢＯＬＩＣＦＩＸＥＤＰＯＩＮＴＯＦＲＥＶＥＲＳＩＢＬＥＭＡＰＰＩＮＧＳ￥ＬＩＵＢＩＮ；ＹＯＵＪＩＡＮＧＯＮＧＡｂｓｔｒａｃｔ：ＫＡＭｔｈｅｏｒｅｍｏｆｒｅｖｅｒｓｉｂｌｅｓｙｓｔｅｍｉｓｕｓｅｄｔｏｐｒｏｖｉｄｅａｓｕ...     

公共不动点定理

本文在Ｈａｕｓｄｏｒｆｆ一致度量空间上首先定义了偏序 ,再利用Ｋｎａｓｔｅｒ－Ｔａｒｓｋｉ原理建立了广义压缩映射的公共不动点定理．     

FURTHER INVESTIGATION INTO APPROXIMATION OF A COMMON SOLUTION OF FIXED POINT PROBLEMS AND SPLIT FEASIBILITY PROBLEMS

The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ? of the split feasibility problem and the set F(T)of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of puniformly convex Banach spaces which are also uniformly smooth.By combining Mann's iterative method and the Halpern's approximation method,we propose an iterative algorithm for finding an element of the set F(T) ∩ ?;moreover,we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method.Our results extend and complement many known related results in the literature.     

ITERATIVE APPROXIMATION OF FIXED POINTS OF NON-LIPSCHITZIAN ASYMPTOTICALLY PSEUDOCONTRACTIVE MAPPINGS

The purpose of this paper is to investigate the problem of approximating fixed points of non-Lipschitizian asymptotically pseudocontractive mappings in an arbitrary real Banach space by the modified Ishikawa iterative sequences with errors.     

CHEBYSHEV APPROXIMATION BY LINEAR ALTERNATING FAMILIES WITH FIXED VALUES AT NODES

In this paper the author discusses a problem of Chebyshev approximation by linear alternating families with fixed values at nodes and gives the analogues of all results for the classical Chebyshev approximation, which include the theorems on existence, alternation, uniqueness, strong uniqueness and the continuty of the best approximation operator, etc.     

COMMON FIXED POINTS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS

For a subset K of a metric space (X , d) and x ∈ X ,P K (x) ={y ∈ K : d(x, y) = d(x, K) ≡ inf { d(x, k) : k ∈ K }}is called the set of best K-approximant to x. An element g。∈ K is said to be a best simultaneous approximation of the pair y 1 , y 2 ∈ X if max{d(y 1 , g。), d(y 2 , g。) } = inf g ∈ K max { d(y 1 , g), d(y 2 , g)}.In this paper, some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved. For self mappings T and S on K, results are proved on both T - and S- invariant points for a set of best simultaneous approximation. Some results on best K-approximant are also deduced. The results proved generalize and extend some results of I. Beg and M. Abbas [1] , S. Chandok and T.D. Narang [2] , T.D. Narang and S. Chandok [11] , S.A. Sahab, M.S. Khan and S. Sessa [14] , P. Vijayaraju [20] and P. Vijayaraju and M. Marudai [21] .     

集值映射的不动点指数与带间断非线性项的椭圆型方程的多重解

<正> 本文研究二阶半线性椭圆边值问题■的多重解(符号详见§3),其中φ(x,t)允许对t是不连续的.一些自由边界问题可以化归这类问题.为了统一处理φ(x,t)对t连续与不连续两种情形,我们采用集值映射的观点.为此推广了经典的算子与Hammerstein算子到集值映射,并发展了集值映射的Leray-Schauder度理论;与已有的集值映射理论不同,现在处理的是映射串(定     

某些非线性映射不动点的迭代逼近

本文讨论Banach空间中拟压缩映射、广义拟压缩映射和广义非扩张映射不动点的迭代逼近,所得结果是[1—3]中相应结果的推广和改进。 定理 1.设E是Banach空间X的非空闭凸子集,T是映E到自身的拟压缩映射,即存在常数q(0≤q<1),使得对于任意x,y∈E,有     

一类非线性非紧算子不动点定理的推广及其应用

本文研究了一类非线性非紧算子不动点定理.利用锥理论,在不需要非线性项满足连续性和紧性条件下,获得无穷区间上Frodholm型积分方程解的存在唯一性,并给出逼近解迭代序列的误差估计.     

FIXED POINT THEOREMS OF GENERALIZED CONTRACTIVE TYPE MAPPINGS(Ⅱ)

In this paper the author obtains several new fixed point theorems for generalized contractive type mappings by means of Kwapisz's contractive gauge function and then proves that lots of contractive type mappings are topologically equivalent to Banach contraction with given contractive constant C∈[0, 1).     

Banach空间中的平均非扩张映象:不动点的存在定理

<正> 设X是Banach空间,E是X中的集合,T是映集合E到自身的映象.若T满足条件(称为平均非扩张条件)其中x,y∈E,a,b,c≥0且a+2b+2c≤1,则称T是平均非扩张映象. 文[1]概括了近年来研究关于平均非扩张映象不动点的一些主要结果.本文进