On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxed η−α Monotone Mapping
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 th...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/207845 |
| Summary: | 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. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |