Convergence Theorems of φ-pseudo Contractive Type Mappings in Normed Linear Spaces

In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.

APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.

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].

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.

SOME CONVERGENCE PROBLEM OF ITERATIVE SEQUENCESFOR ACCRETIVE AND PSEUDO-CONTRACTIVETYPE MAPPING IN BANACH SPACES

Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, extend and include some recent results.

CQ Method for Strictly Pseudo-Contractive Mapping

This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only O-strictly pseudo-contractive, the main result obtained in this paper extends the corresponding main result of Nakajo-Takahashi from non-expansive mapping to k-strictly pseudo-contractive one, where k∈ [0,1）.

A Modified Averaging Composite Implicit Iteration Process for Common Fixed Points of a Finite Family of k-Strictly Asymptotically Pseudocontractive Mappings

The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process.

Approximative Method of Fixed Point for Φ-Pseudocontractive Operator and an Application to Equation with Accretive Operator

In this paper, Φ-pseudo-contractive operators and Φ-accretive operators, more general than the strongly pseudo-contractive operators and strongly accretive operators, are introduced. By setting up a new inequality, authors proved that if ?is a uniformly continuous Φ-pseudo-contractive operator then T has unique fixed point q and the Mann iterative sequence with random errors approximates to q. As an application, the iterative solution of nonlinear equation with Φ-accretive operator is obtained. The results presented in this paper improve and generalize some corresponding results in recent literature.

APPROXIMATION OF FIXED POINTS OF STRICTLY PSEUDO-CONTRACTIVE MAPPING WITHOUT LIPSCHITZ ASSUMPTION

Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces, the Ishikawa iteration ｛x n｝ ∞ n=1 defined byx 1∈K,\ x n+1 =(1-α n)x n+α nTy n,\ y n=(1-β n)x n+β nTx n,\ n≥1satisfying 0<α n,β n<1 ,for all n≥1;∑ ∞ n=1 α n=∞;α n→0,β n→0 as n→∞ is proved to converge strongly to the unique fixed point of T ,where T:K→K is a uniformly continuous strictly pseudo\|contractive operator with bounded range.

Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces

The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.

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.

混合Bregman投影算法在Banach空间中分裂不动点问题的强收敛性

在p-一致凸且一致光滑的Banach空间中,利用Bregman投影,构造一新的混合投影迭代算法,逼近Bregman拟严格伪压缩映射不动点集和分裂可行性问题的公共解.目的是将2017年Chen J Z,Hu H Y和Ceng L C的研究结果中的迭代系数α_(n)须满足0<c≤a_(n)≤d<1证明对α_(n)≡1或α_(n)≡0时亦成立.所得的结果是对2017年Chen J Z,Hu H Y和Ceng L C相应结果的拓展和补充.

伪压缩型映象迭代逼近的收敛性问题

研究一类伪压缩型映象迭代逼近的收敛性问题 。

Φ-伪压缩映象迭代序列的收敛性与稳定性

在没有T(D)=∪_(x∈D)Tx有界条件下,在实Banach空间中研究了广义Lipschitz Φ-伪压缩映象不动点的带混合型误差的Ishikawa和Mann迭代序列的逼近问题,使用新的分析方法,建立了带混合型误差的Ishikawa和Mann迭代序列的收敛性与稳定性定理,从而推广和改进了一些已知结果.

关于Lipschitz拟伪压缩映像族的强收敛定理

在Hilbert空间中设计出2种新的关于Lipschitz拟伪压缩映像族和严格拟伪压缩映像族的收缩投影算法,并利用所提出的算法证明了Lipschitz拟伪压缩映像族和严格拟伪压缩映像族的公共不动点的强收敛定理,所得结果改进和推广了已有文献的相关结果.

关于拟渐近伪压缩映像族的复合迭代算法

在Hilbert空间中设计出一种新的关于拟渐近伪压缩映像族的复合迭代算法,并利用所提出的算法证明了一致Lipschitz拟渐近伪压缩映像族之强收敛定理成立,最后给出具体的数值实验说明所提出算法的有效性。得到的结论改进了最新文献的一些研究成果。

一致Φ-伪压缩映像不动点的迭代逼近

修改了Ishikawa和Mann迭代序列,研究了一致φ-伪压缩映像不动点的迭代收敛问题,改进和发展了一系列相应结果.

Hilbert空间中闭的拟严格伪压缩映像的收缩投影方法(英文)

在Hilbert空间中,引入和研究了一种新的收缩投影迭代算法,用以逼近拟严格伪压缩映像的不动点.在适当的条件下,利用所提出的收缩投影算法证明了闭的拟严格伪压缩映像的不动点的强收敛定理,所得结果改进和推广了近期文献的相关结果.

带误差的非扩张映象及强伪压缩映象的Ishikawa迭代序列的收敛性

主要研究了带误差的非扩张映象及强伪压缩映象的Ishikawa迭代序列的收敛性问题,推广了已知的相关结果.

受迫摆方程的伪概周期解

利用伪概周期函数的性质和Banach压缩映像原理研究受迫摆方程的伪概周期解问题,证明伪概周期解的存在性及在条件‖y-π‖L∞<π2下的唯一性。