STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF STRICT PSEUDO-CONTRACTION MAPPINGS

ZHAO , LIANG CAI ¹ ; CHANG, SHIH-SEN²

¹ Department of Mathematics, Yibin University, Yibin, Sichuan 644000, China
² Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China

Journal of nonlinear sciences and its applications, Tome 2 (2009) no. 2, p. 78-91.

Résumé

The purpose of this paper is to introduce an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a k−strict pseudo-contraction non-self mapping in Hilbert space. By the viscosity approximation algorithms, under suitable conditions , some strong convergence theorems for approximating to this common elements are proved. The results presented in the paper extend and improve some recent results of Marino and Xu [G.Marino,H.K.Xu, Weak and strong convergence theorems for k−strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336–349], Zhou [H.Zhou, Convergence theorems of fixed Points for k−strict pseudo-contractions in Hilbert spaces, Nonlinear Anal. 69 (2008) 456–462], Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506– 515], Ceng,Homidan,etc [L. C. Ceng, S.A.Homidan, Q.H.Ansari, J. C. Yao, An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings, J. Comput. Appl. Math. 223 (2009) 967–974].

Détail

DOI : 10.22436/jnsa.002.02.02

Classification : 47H05, 47H09, 47H10
Keywords: Equilibrium problem, strict pseudo-contraction mapping, fixed point, strong convergence theorem.

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