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On the Solution Existence of Variational‐Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping

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  • Marwan Amin Kutbi
  • Wutiphol Sintunavarat

Abstract

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

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:207845
DOI: 10.1155/2013/207845
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