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Well‐Posedness for a Class of Strongly Mixed Variational‐Hemivariational Inequalities with Perturbations

Author

Listed:
  • Lu-Chuan Ceng
  • Ngai-Ching Wong
  • Jen-Chih Yao

Abstract

The concept of well‐posedness for a minimization problem is extended to develop the concept of well‐posedness for a class of strongly mixed variational‐hemivariational inequalities with perturbations which includes as a special case the class of variational‐hemivariational inequalities with perturbations. We establish some metric characterizations for the well‐posed strongly mixed variational‐hemivariational inequality and give some conditions under which the strongly mixed variational‐hemivariational inequality is strongly well‐posed in the generalized sense. On the other hand, it is also proven that under some mild conditions there holds the equivalence between the well posedness for a strongly mixed variational‐hemivariational inequality and the well‐posedness for the corresponding inclusion problem.

Suggested Citation

  • Lu-Chuan Ceng & Ngai-Ching Wong & Jen-Chih Yao, 2012. "Well‐Posedness for a Class of Strongly Mixed Variational‐Hemivariational Inequalities with Perturbations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:712306
    DOI: 10.1155/2012/712306
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    References listed on IDEAS

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    1. Eberhard Zeidler, 1990. "Nonlinear Functional Analysis and its Applications," Springer Books, Springer, number 978-1-4612-0981-2, March.
    2. X. X. Huang, 2001. "Extended and strongly extended well-posedness of set-valued optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 101-116, April.
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