Fixed points of multivalued nonexpansive mappings in Banach spaces
1 Department of Mathematics, Statistics and Physics,Qatar University, Doha 2713, Qatar
2 Department of Mathematics, Ataturk University, Erzurum 25240, Turkey
Fixed Point Theory and Applications 2012, 2012:73 doi:10.1186/1687-1812-2012-73Published: 2 May 2012
In this article, we first give a multivalued version of an iteration scheme of Agarwal et al. We use an idea due to Shahzad and Zegeye which removes a "strong condition" on the mapping involved in the iteration scheme and an observation by Song and Cho about the set of fixed points of that mapping. In this way, we approximate fixed points of a multivalued nonexpansive mapping through an iteration scheme which is independent of but faster than Ishikawa scheme used both by Song and Cho, and Shahzad and Zegeye. Thus our results improve and unify corresponding results in the contemporary literature.
Mathematics Subject Classification (2000): 47H10; 54H25.