Abstract
Let H be a real Hilbert space and K a nonempty closed convex subset of H. Suppose T:K→CB(K) is a multivalued Lipschitz pseudocontractive mapping such that F(T)≠∅. An Ishikawa-type iterative algorithm is constructed and it is shown that, for the corresponding sequence {xn}, under appropriate conditions on the iteration parameters, lim infn→∞ d (xn,Txn)=0 holds. Finally, convergence theorems are proved under approximate additional conditions. Our theorems are significant improvement on important recent results of Panyanak (2007) and Sastry and Babu (2005).
Highlights
Let K be a nonempty subset of a normed space E
Chidume et al [15] introduced the class of multivalued strictly pseudocontractive maps defined on a real Hilbert space H as follows
This proves that T is not nonexpansive. It is our purpose in this paper to prove strong convergence theorems for the class of multivalued Lipschitz pseudocontractive maps in real Hilbert spaces
Summary
Let K be a nonempty subset of a normed space E. Let H be real Hilbert space, K a nonempty compact convex subset of H, and T : K → P(K) a multivalued nonexpansive map with a fixed point p.
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