Strong convergence theorems for a finite family of asymptotically nonexpansive mappings and semigroups

Strong convergence theorems are obtained for a finite family of asymptotically nonexpansive mappings and semigroups by the modified Mann method.     

Strong convergence theorems for a finite family of asymptotically nonexpansive mappings and semigroups

Strong convergence theorems are obtained for a finite family of asymptotically nonexpansive mappings and semigroups by the modified Mann method.     

An iterative process for a finite family of pseudocontractive mappings

The purpose of this paper is to study the following implicit iteration scheme recently introduced by Xu and Ori [Numer. Funct. Anal. Optim., 22, (2001) 767–773]:

Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings

In this paper, a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of continuous pseudocontractive mappings are proved in an arbitrary real Banach space using an implicit iteration scheme recently introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Fuct. Anal. Optim. 22 (2001) 767-773] in condition αn∈(0,1], and also strong and weak convergence theorem of a finite family of strictly pseudocontractive mappings of Browder-Petryshyn type is obtained. The results presented extend and improve the corresponding results of M.O. Osilike [M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004) 73-81].     

凸度量空间中两无限族严格拟渐近伪压缩映象公共不动点的逼近

凸度量空间中,引入了（λ,{kn}）-严格拟渐近伪压缩映象.并且讨论了两无限族严格拟渐近伪压缩映象公共不动点的逼近问题.在适当的条件下,证明了一些强收敛定理.改进了和推广一些文献的结果.     

Strong convergence theorems by hybrid methods for a finite family of nonexpansive mappings and inverse-strongly monotone mappings

In this paper, we introduce and study an iterative scheme by a hybrid method for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a real Hilbert space. Then, we prove that the iterative sequence converges strongly to a common element of the three sets. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.     

The new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings

Convergence theorems for approximation of common fixed points of strictly pseudocontractive mappings of Browder-Petryshyn type are proved in Banach spaces using a new composite implicit iteration scheme with errors. The results presented in this paper generalize and improve the corresponding results of M.O. Osilike [M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004) 73-81].     

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 viscosity 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 nonlinear 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.     

Strong convergence theorems for a finite family of nonexpansive mappings and semigroups via the hybrid method

Strong convergence theorems are obtained for a finite family of nonexpansive mappings and semigroups by the hybrid method.     

Weak and strong convergence theorems of an implicit iteration for a countable family of continuous pseudocontractive mappings

To approximate a common fixed point of a countable family of continuous pseudocontractive mappings, we introduce an implicit iteration sequence. A necessary and sufficient condition for the convergence of a sequence of such iterates for countably many continuous pseudocontractive mappings is given. We also prove the convergence theorems of an implicit iteration sequence for a countable family of strictly pseudocontractive mappings.     

Two kinds of Novikov algebras and their realizations

In this paper, we construct two kinds of Novikov algebras, characterize some properties of them and give their realizations by triangle functions, respectively.     

On iterations for families of asymptotically pseudocontractive mappings

In this work, we establish strong convergence for a modified multistep iterative scheme associated with families of mappings in real Banach spaces. Moreover, our technique of proof is of independent interest. A remark at the end simplifies many known results.     

Extragradient algorithms for equilibrium problems and symmetric generalized hybrid mappings

In this paper, we propose new algorithms for finding a common point of the solution set of a pseudomonotone equilibrium problem and the set of fixed points of a symmetric generalized hybrid mapping in a real Hilbert space. The convergence of the iterates generated by each method is obtained under assumptions that the fixed point mapping is quasi-nonexpansive and demiclosed at 0, and the bifunction associated with the equilibrium problem is weakly continuous. The bifunction is assumed to be satisfying a Lipschitz-type condition when the basic iteration comes from the extragradient method. It becomes unnecessary when an Armijo back tracking linesearch is incorporated in the extragradient method.     

A general iterative method for a finite family of nonexpansive mappings

We study the approximation of common fixed points of a finite family of nonexpansive mappings and suggest a modification of the iterative algorithm without the assumption of any type of commutativity. Also we show that the convergence of the proposed algorithm can be proved under some types of control conditions.     

Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps

Convergence theorems for approximation of common fixed points of strictly pseudocontractive mappings of Browder-Petryshyn type are proved in Banach spaces using an implicit iteration scheme recently introduced by Xu and Ori [Numer. Funct. Anal. Optim. 22 (2001) 767-773].     

Composite implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps

Let E be a real Banach space and let K be a nonempty closed convex subset of E. Let be N strictly pseudocontractive self-maps of K such that , where F(T_i)={xK:T_ix=x} and let be two real sequence satisfying the conditions:

where L1 is common Lipschitz constant of . For x₀K, let be new implicit process defined by

x_n=α_nx_n−1+(1−α_n)T_ny_n,