Multiple-set split feasibility problems for total asymptotically strict pseudocontractions mappings

Li Yang, Chang Shih-Sen, Cho, Kim

Description

The purpose of this article is to propose and investigate an algorithm for solving the multiple-set split feasibility problems for total asymptotically strict pseu-docontractions mappings in infinite-dimensional Hilbert spaces . The results presented in this article improve and extend some recent results of A. Moudafi, H. K. Xu, Y. Censor, A. Segal, T. Elfving, N. Kopf, T. Bortfeld, X. A. Motova, Q. Yang, A. Gibali, S. Reich and others. 2000 AMS Subject Classification : 47J05; 47H09; 49J25.

Informations

• Publié par: biomed
• Publié le: 01 janvier 2011
• Nombre de lectures: 3
• Langue: English

Extrait

Yanget al.Fixed Point Theory and Applications2011,2011:77 http://www.fixedpointtheoryandapplications.com/content/2011/1/77

R E S E A R C HOpen Access Multipleset split feasibility problems for total asymptotically strict pseudocontractions mappings 1* 2*3 4 LI Yang, ShihSen Chang, Yeol JE Choand Jong KYU Kim

* Correspondence: [e-mail]; [e-mail] 1 Department of Mathematics, South West University of Science and Technology, Mianyang Sichuan 621010, China 2 College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China Full list of author information is available at the end of the article

Abstract The purpose of this article is to propose and investigate an algorithm for solving the multipleset split feasibility problems for total asymptotically strict pseudocontractions mappings in infinitedimensional Hilbert spaces. The results presented in this article improve and extend some recent results of A. Moudafi, H. K. Xu, Y. Censor, A. Segal, T. Elfving, N. Kopf, T. Bortfeld, X. A. Motova, Q. Yang, A. Gibali, S. Reich and others. 2000 AMS Subject Classification: 47J05; 47H09; 49J25. Keywords:multipleset split feasibility problem, split feasibility problem, demiclose ness, Opial condition, total asymptotically strict pseudocontraction

1. Introduction and preliminaries Throughout this article, we always assume thatH 1 ,H 2 are real Hilbert spaces,“®”,“⇀” are denoted by strong and weak convergence, respectively, andF(T) is the fixed point set of a mappingT. LetGbe a nonempty closed convex subset ofH 1 andT:G®Ga mapping. Tis said to be a contraction if there exists a constantaÎ(0,1) such that T x −T y ≤αx−y,∀x,y∈G (1:1) Banach contraction principle guarantees that every contractive mapping defined on complete metric spaces has a unique fixed point. Tis said to be a weak contraction if      T x −T y ≤x−y−ψx−y,∀x,y∈G (1:2) whereψ: [0,∞)®[0,∞) is a continuous and nondecreasing function such thatψis positive on (0,∞),ψ(0) = 0, and lim t®∞ ψ(t) =∞. We remark that the class of weak contractions was introduced by Alber and GuerreDelabriere [1]. In 2001, Rhoades [2] showed that every weak contraction defined on complete metric spaces has a unique fixed point. Tis said to be nonexpansive if   T x −T y ≤x−y,∀x,y∈G (1:3)

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