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Further Investigation on the Relaxed Hybrid Steepest‐Descent Methods for Variational Inequalities with k‐Strict Pseudocontractions

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  • Qian-Fen Gong
  • Dao-Jun Wen

Abstract

We modify the relaxed hybrid steepest‐descent methods to the case of variational inequality for finding a solution over the set of common fixed points of a finite family of strictly pseudocontractive mappings. The strongly monotone property defined on cost operator was extended to relaxed cocoercive in convergence analysis. Results presented in this paper may be viewed as a refinement and important generalizations of the previously known results announced by many other authors.

Suggested Citation

  • Qian-Fen Gong & Dao-Jun Wen, 2014. "Further Investigation on the Relaxed Hybrid Steepest‐Descent Methods for Variational Inequalities with k‐Strict Pseudocontractions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:381592
    DOI: 10.1155/2014/381592
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    References listed on IDEAS

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    1. Eberhard Zeidler, 1985. "Nonlinear Functional Analysis and its Applications," Springer Books, Springer, number 978-1-4612-5020-3, March.
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