Fejér monotone sequences and nonexpansive mappings

The notion of Fejér monotonicity has proven to be a fruitful concept in fixed point theory and optimization. In this paper, we present new conditions sufficient for convergence of Fejér monotone sequences and we also provide applications to the study of nonexpansive mappings. Various examples illustrate our results. 2010 Mathematics Subject Classification: Primary 47H09; Secondary 47H05, 90C25.