On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxedη−αMonotone Mapping | Zendy

Marwan Amin Kutbi | Zendy; Wutiphol Sintunavarat | Zendy

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On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxedη−αMonotone Mapping

Author(s) -

Marwan Amin Kutbi,

Wutiphol Sintunavarat

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/207845

Subject(s) - algorithm , monotone polygon , banach space , variational inequality , mathematics , computer science , discrete mathematics , geometry

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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