THREE TYPES OF VARIATIONAL RELATION PROBLEMS

Variational relation problems were introduced by Luc in [1] as a general model for a large class of problems in nonlinear analysis and applied mathematics. Since this manner of approach provides unified results for several mathematical problems it has been used in many recent papers (see [2-9]). In...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 17; no. 1; pp. 47 - 61
Main Author Balaj, Mircea
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.02.2013
Subjects
Existence theorems
Index sets
Mathematical inequalities
Mathematical relations
Mathematical theorems
Mathematical vectors
Topological spaces
Topological theorems
Topological vector spaces
Variational inequalities
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Summary:Variational relation problems were introduced by Luc in [1] as a general model for a large class of problems in nonlinear analysis and applied mathematics. Since this manner of approach provides unified results for several mathematical problems it has been used in many recent papers (see [2-9]). In this paper we investigate the existence of solutions for three types of variational relation problems which encompass several generalized equilibrium problems, variational inequalities and variational inclusions studied in a long list of papers in the field. 2010Mathematics Subject Classification: 49J53, 54H25. Key words and phrases: Variational relation problem, Variational inequality, KKM theorem, Fixed point.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.17.2013.1558