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Iterative Schemes for Solving Mixed Variational-Like Inequalities

Author

Listed:
  • Q. H. Ansari

    (Aligarh Muslim University)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

In the present paper, we introduce the concept of η-cocoercivity of a map and develop some iterative schemes for finding the approximate solutions of mixed variational-like inequalities. We use the concept of η-cocoercivity to prove the convergence of the approximate solutions to the exact solution of mixed variational-like inequalities.

Suggested Citation

  • Q. H. Ansari & J. C. Yao, 2001. "Iterative Schemes for Solving Mixed Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 527-541, March.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:3:d:10.1023_a:1017531323904
    DOI: 10.1023/A:1017531323904
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    Citations

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    Cited by:

    1. L. C. Ceng & N. Hadjisavvas & S. Schaible & J. C. Yao, 2008. "Well-Posedness for Mixed Quasivariational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 109-125, October.
    2. Lu-Chuan Zeng & Jen-Chih Yao, 2005. "Convergence analysis of a modified inexact implicit method for general mixed monotone variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 211-224, November.
    3. 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.
    4. L. C. Zeng & S. Schaible & J. C. Yao, 2005. "Iterative Algorithm for Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 725-738, March.
    5. Nicuşor Costea & Daniel Alexandru Ion & Cezar Lupu, 2012. "Variational-Like Inequality Problems Involving Set-Valued Maps and Generalized Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 79-99, October.
    6. S. Schaible & J. C. Yao & L. C. Zeng, 2006. "Iterative Method for Set-Valued Mixed Quasi-variational Inequalities in a Banach Space," Journal of Optimization Theory and Applications, Springer, vol. 129(3), pages 425-436, June.
    7. 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.
    8. Imran Ali & Rais Ahmad & Ching-Feng Wen, 2019. "Cayley Inclusion Problem Involving XOR-Operation," Mathematics, MDPI, vol. 7(3), pages 1-12, March.

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