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Variational Inequalities and Fixed Point Theorems for PM-Maps

โœ Scribed by Kunquan Lan; Jeffrey Webb

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
184 KB
Volume
224
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

We study maps T for which J y T is pseudo-monotone; we call such T a PM-map. This includes compact maps in suitable spaces and pseudo-contractive maps in Hilbert spaces. We study variational inequalities in a situation which was previously done only when T is compact. We show that our variational inequalities ลฝ are well suited to treating existence of fixed points for generalized inward in . particular, weakly inward PM-maps in Hilbert spaces. Our new results on existence of fixed points generalizes many earlier results obtained by using other methods. An application to homogeneous integral equations is provided. แฎŠ 1998

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