Journal of Optimization Theory and Applications

, Volume 133, Issue 3, pp 359–370

Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem

Article

DOI: 10.1007/s10957-007-9187-z

Cite this article as:
Tada, A. & Takahashi, W. J Optim Theory Appl (2007) 133: 359. doi:10.1007/s10957-007-9187-z

Abstract

In this paper, we introduce two iterative sequences for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem in a Hilbert space. Then, we show that one of the sequences converges strongly and the other converges weakly.

Keywords

Equilibrium problems Nonexpansive mappings Firmly nonexpansive mappings Weak and strong convergence Monotonicity 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan

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