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1.
The purpose of this article is to prove some approximation theorems of common fixed points for countable families of total quasi-?-asymptotically nonexpansive mappings which contain several kinds of mappings as its special cases in Banach spaces. In order to get the approximation theorems, the hybrid algorithms are presented and are used to approximate the common fixed points. Using this result, we also discuss the problem of strong convergence concerning the maximal monotone operators in a Banach space. The results of this article extend and improve the results of Matsushita and Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theor. 134 (2005) 257-266], Plubtieng and Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces, J. Approx. Theor. 149 (2007) 103-115], Li, Su [H. Y. Li, Y. F. Su, Strong convergence theorems by a new hybrid for equilibrium problems and variational inequality problems, Nonlinear Anal. 72(2) (2010) 847-855], Su, Xu and Zhang [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890-3960], Wang et al. [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364-2371], Chang et al. [S.S. Chang, H.W. Joseph Lee, Chi Kin Chan, A new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in Banach spaces with applications, Nonlinear Anal. 73 (2010) 2260-2270], Chang et al. [S.S. Chang, C.K. Chan, H.W. Joseph Lee, Modified block iterative algorithm for quasi-?-asymptotically nonexpansive mappings and equilibrium problem in Banach spaces, Appl. Math. Comput. 217 (2011) 7520-7530], Ofoedu and Malonza [E.U. Ofoedu, D.M. Malonza, Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type, Appl. Math. Comput. 217 (2011) 6019-6030] and Yao et al. [Y.H. Yao, Y.C. Liou, S.M. Kang, Strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings, Appl. Math. Comput. 208 (2009) 211-218].  相似文献   

2.
The purpose of this paper is to introduce a hybrid projection algorithm based on the shrinking projection method for two relatively weak nonexpansive mappings. We prove strong convergence theorem which approximate the common element in the fixed point set of two such mappings, the solution set of the variational inequality and the solution set of the equilibrium problem in the framework of Banach spaces. Our results improve and extend previous results.  相似文献   

3.
The purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi-?-asymptotically nonexpansive mappings and the set of an equilibrium problem. Under suitable conditions, some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with the Kadec-Klee property. As an application, at the end of the paper a numerical example is given. The results presented in the paper improve and extend the corresponding results in Qin et al. [Convergence theorems of common elements for equilibrium problems and fixed point problem in Banach spaces, J. Comput. Appl. Math., 225, 2009, 20-30], Zhou et al. [Convergence theorems of a modified hybrid algorithm for a family of quasi-?-asymptotically nonexpansive mappings, J. Appl. Math. Compt., 17 March, 2009, doi:10.1007/s12190-009-0263-4], Takahashi and Zembayshi [Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal., 70, 2009, 45-57], Wattanawitoon and Kumam [Strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Anal. Hybrid Syst., 3, 2009, 11-20] and Matsushita and Takahashi [A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theory, 134, 2005, 257-266] and others.  相似文献   

4.
The purpose of this article is to modify the Halpern-type iteration algorithm for total quasi-?-asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results of [X.L. Qin, Y.J. Cho, S.M. Kang, H. Y. Zhou, Convergence of a modified Halpern-type iterative algorithm for quasi-?-nonexpansive mappings, Appl. Math. Lett. 22 (2009) 1051-1055], [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364-2371], [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890-3906], [C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and others.  相似文献   

5.
Let E be a real normed linear space, K be a nonempty subset of E and be a uniformly continuous generalized Φ-hemi-contractive mapping, i.e., , and there exist xF(T) and a strictly increasing function , Φ(0)=0 such that for all xK, there exists j(xx)∈J(xx) such that
Txx,j(xx)〉?‖xx2Φ(‖xx‖).  相似文献   

6.
In this paper, we modify the set of variational inequality to construct a new iterative scheme for finding a common element of the set of fixed point problems of infinite family of κ i -pseudo-contractive mappings and the set of equilibrium problem and two set of variational inequality problems.  相似文献   

7.
In this paper, we consider a hybrid projection method for finding a common element in the set of fixed points of a infinite family of asymptotically quasi-?-nonexpansive mappings and in the set of solutions of a generalized mixed equilibrium problem. Some strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. The results presented in the paper improve and extend some recent results.  相似文献   

8.
9.
The purpose of this paper is to prove weak and strong convergences of a modified implicit iteration process to common fixed points for a finite family of asymptotically nonexpansive mappings. The results presented in this paper improve and extend some well known results.  相似文献   

10.
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.  相似文献   

11.
The purpose of this article is to propose a modified hybrid projection algorithm and prove strong convergence theorems for a family of quasi-φ-asymptotically nonexpansive mappings. The results of this paper improve and extend the results of S. Matsushita and W. Takahashi (J. Approx. Theory, 134: 257–266 (2005)), T.H. Kim, H.K. Xu (Nonlinear Anal. 64: 1140–1152 (2006)), Y.F. Su, D.X. Wang, M.J. Shang (Fixed Point Theory Appl. 2008: 284613 (2008)) and others.  相似文献   

12.
In this paper, we present a new self-adaptive alternating direction method for solving a class of variational inequality problems with both linear equality and inequality constraints without the need to add any extra slack variables. The method is simple because it needs only to perform some projections and function evaluations. In addition, to further enhance its efficiency, we adopt a self-adaptive strategy to adjust parameter μ at each iteration. Convergence of the proposed method is proved under certain conditions. Numerical experience illustrates the efficiency of the new method.  相似文献   

13.
We prove (L p , L q ) inequalities for mixed moduli of smoothness of positive orders. As corollaries, we obtain embedding theorems for the Nikol’skii classes.  相似文献   

14.
We use the critical point theory for convex, lower semicontinuous perturbations of C1-functionals to establish existence of multiple radial solutions for some one parameter Neumann problems involving the operator . Similar results for periodic problems are also provided.  相似文献   

15.
A new approach using the over-relaxed proximal point algorithm in the context of solving a class of inclusion problems based on the notion of maximal (η)-monotonicity is developed and examined. Convergence analysis seems to be reasonable, and finally, some specializations are included. Furthermore, the model developed in this communication seems to be appropriate to the Yosida approximation in the sense that it can be applied to first-order evolution equations/inclusions as well.  相似文献   

16.
By using the Φ-entropy inequality derived in [16] and [2] for Poisson measures, the same type of inequality is established for a class of stochastic differential equations driven by purely jump Lévy processes. This inequality implies the exponential convergence in Φ-entropy of the associated Markov semigroup. The semigroup Φ-entropy inequality for SDEs driven by Poisson point processes is also considered.  相似文献   

17.
Using Leray-Schauder degree theory we obtain various existence and multiplicity results for nonlinear boundary value problems
  相似文献   

18.
In this paper we correct an error which appeared in Theorem 4.1 in Aussel and Dutta (2008). We also provide an example to illustrate our point.  相似文献   

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