A new two step iterative scheme for a finite family of nonself I-asymptotically nonexpansive mappings in Banach space

Abstract

Let E be a real uniformly convex Banach space, K be a nonempty closed convex subset of E and let Ti : K → E be N Ii-asymptotically nonexpansive nonself mappings and Ii be N asymptotically nonexpansive nonself mappings. It is proved that a new two step iterative algorithm converges weakly to a q ∈ F in a real uniformly convex Banach space such that its dual has the Kadec-Klee property and strongly under condition (B) in a real uniformly convex Banach space. It presents some new results in this paper.

Keywords

• Nonself I-asymptotically nonexpansive mapping,Fr´echet differentiable norm,Opial property,Kadec-Klee property,B condition

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