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On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed Monotone Mapping

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  • Marwan Amin Kutbi
  • Wutiphol Sintunavarat

Abstract

We introduce two new concepts of weakly relaxed monotone mappings and weakly relaxed semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed monotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxed semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem.

Suggested Citation

  • Marwan Amin Kutbi & Wutiphol Sintunavarat, 2013. "On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed Monotone Mapping," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, November.
    • Handle: RePEc:hin:jnlaaa:207845
    DOI: 10.1155/2013/207845
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