Journal of Global Optimization

, Volume 54, Issue 1, pp 185–197 | Cite as

Viscosity approximation methods for a nonexpansive semigroup in Banach spaces with gauge functions

Article
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Abstract

We first investigate strong convergence of the sequence generated by implicit and explicit viscosity approximation methods for a one-parameter nonexpansive semigroup in a real Banach space E which has a uniformly Gâteaux differentiable norm and admits the duality mapping j φ , where φ is a gauge function on [0, ∞). The main results also improve and extend some known results concerning the normalized duality mapping in the literature.

Keywords

Banach spaces Common fixed points Gauge functions Implicit and explicit viscosity methods Nonexpansive semigroup 

Mathematics Subject Classification (2000)

47H09 47H10 
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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.School of ScienceUniversity of PhayaoPhayaoThailand
  2. 2.Department of Mathematics, Faculty of ScienceChiang Mai UniversityChiang MaiThailand
  3. 3.Materials Science Research Center, Faculty of ScienceChiang Mai UniversityChiang MaiThailand

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