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Existence of Solutions and an Algorithm for Mixed Variational-Like Inequalities in Banach Spaces

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  • X. P. Ding

    (Sichuan Normal University)

Abstract

In this paper, we study the class of mixed variational-like inequalities in reflexive Banach spaces. By applying a minimax inequality due to the author, some existence and uniqueness theorems for solutions of mixed variational-like inequalities are proved. Next, by applying the auxiliary problem technique, we suggest an innovative iterative algorithm to compute approximate solutions of the mixed variational-like inequality. Finally, convergence criteria are also discussed.

Suggested Citation

  • X. P. Ding, 2005. "Existence of Solutions and an Algorithm for Mixed Variational-Like Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 127(2), pages 285-302, November.
    • Handle: RePEc:spr:joptap:v:127:y:2005:i:2:d:10.1007_s10957-005-6540-y
    DOI: 10.1007/s10957-005-6540-y
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    Cited by:

    1. Shamshad Husain & Sanjeev Gupta & Vishnu Narayan Mishra, 2013. "Generalized -Cocoercive Operators and Generalized Set-Valued Variational-Like Inclusions," Journal of Mathematics, Hindawi, vol. 2013, pages 1-10, June.
    2. X. Ding & Y. Liou & J. Yao, 2012. "Existence and algorithms for bilevel generalized mixed equilibrium problems in Banach spaces," Journal of Global Optimization, Springer, vol. 53(2), pages 331-346, June.
    3. X. P. Ding, 2012. "Auxiliary Principle and Algorithm of Solutions for a New System of Generalized Mixed Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 796-809, December.

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