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


  • Prasit Cholamjiak


  • Suthep Suantai



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. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Prasit Cholamjiak & Suthep Suantai, 2012. "Viscosity approximation methods for a nonexpansive semigroup in Banach spaces with gauge functions," Journal of Global Optimization, Springer, vol. 54(1), pages 185-197, September.
  • Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:185-197
    DOI: 10.1007/s10898-011-9756-4

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    References listed on IDEAS

    1. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
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