Minimum‐Norm Fixed Point of Pseudocontractive Mappings

Habtu Zegeye, Naseer Shahzad and Mohammad Ali Alghamdi

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: Let K be a closed convex subset of a real Hilbert space H and let T : K → K be a continuous pseudocontractive mapping. Then for β ∈ (0, 1) and each t ∈ (0, 1), there exists a sequence {yt} ⊂ K satisfying yt = βPK[(1 − t)yt] + (1 − β)T(yt) which converges strongly, as t → 0+, to the minimum‐norm fixed point of T. Moreover, we provide an explicit iteration process which converges strongly to a minimum‐norm fixed point of T provided that T is Lipschitz. Applications are also included. Our theorems improve several results in this direction.

Date: 2012
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https://doi.org/10.1155/2012/926017

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:926017

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