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On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed $\eta \text{-}\alpha $ Monotone Mapping
- Source :
- Abstr. Appl. Anal.
- Publication Year :
- 2013
- Publisher :
- Hindawi Publishing Corporation, 2013.
-
Abstract
- We introduce two new concepts of weakly relaxed $\eta \text{-}\alpha $ monotone mappings and weakly relaxed $\eta \text{-}\alpha $ semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed $\eta \text{-}\alpha $ monotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxed $\eta \text{-}\alpha $ semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem.
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Abstr. Appl. Anal.
- Accession number :
- edsair.project.eucl..2463104648557485e6cac695144df052