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2013 Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces
Jong Soo Jung
Abstr. Appl. Anal. 2013: 1-7 (2013). DOI: 10.1155/2013/369412

Abstract

Let E be a reflexive Banach space having a weakly sequentially continuous duality mapping J φ with gauge function φ , C a nonempty closed convex subset of E , and T : C 𝒦 ( E ) a multivalued nonself-mapping such that P T is nonexpansive, where P T ( x ) = { u x T x : x - u x = d ( x , T x ) } . Let f : C C be a contraction with constant k . Suppose that, for each v C and t ( 0,1 ) , the contraction defined by S t x = t P T x + ( 1 - t ) v has a fixed point x t C . Let { α n } , { β n }, and { γ n } be three sequences in ( 0,1 ) satisfying approximate conditions. Then, for arbitrary x 0 C , the sequence { x n } generated by x n α n f ( x n - 1 ) + β n x n - 1 + γ n P T ( x n ) for all n 1 converges strongly to a fixed point of T .

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Jong Soo Jung. "Convergence of a Viscosity Iterative Method for Multivalued Nonself-Mappings in Banach Spaces." Abstr. Appl. Anal. 2013 1 - 7, 2013. https://doi.org/10.1155/2013/369412

Information

Published: 2013
First available in Project Euclid: 18 April 2013

zbMATH: 1275.47124
MathSciNet: MR3034954
Digital Object Identifier: 10.1155/2013/369412

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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