Convergence on Composite Iterative Schemes for Nonexpansive Mappings in Banach Spaces
© Jong Soo Jung. 2008
Received: 13 January 2008
Accepted: 3 May 2008
Published: 7 May 2008
Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm. Suppose that every weakly compact convex subset of has the fixed point property for nonexpansive mappings. Let be a nonempty closed convex subset of , a contractive mapping (or a weakly contractive mapping), and nonexpansive mapping with the fixed point set . Let be generated by a new composite iterative scheme: , , . It is proved that converges strongly to a point in , which is a solution of certain variational inequality provided that the sequence satisfies and , for some and the sequence is asymptotically regular.
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