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A Counterexample on Implicit Variational Inequalities

โœ Scribed by Sangho Kum

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
107 KB
Volume
215
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

Our aim in this note is to give a counterexample to show that some existence theorems on implicit variational inequalities recently due to Fu are false. แฎŠ 1997 Academic Press w x In a recent paper, Fu 1 considered the following implicit variational problem, denoted by I.V.P.: Let X, Y be topological vector spaces; let C and D be nonempty subsets of X and Y, respectively. Given multivalued mappings E: C ยช 2 C and F: C ยช 2 D , real functions f : C = C = D ยช R ลฝ . ลฝ . and g: C = C ยช R such that for any x g C, y g F x , f x, x, y G 0. Find ลฝ .

ลฝ . a vector ยจg C such that ยจg E ยจand u g F ยจsuch that g ยจ, ยจF f ยจ, w, u q g ยจ, w for all w g E ยจ.

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