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A note on multivalued pseudomonotone map

โœ Scribed by Zijia Peng; Zhenhai Liu

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
209 KB
Volume
24
Category
Article
ISSN
0893-9659

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โœฆ Synopsis

This paper is concerned with a class of W ฮป 0 pseudomonotone maps given by Kasyanov et al. ( , 2006) [2,15]) [2,15]. We indicate that its main character of passing to a subsequence in classical definition is meaningless. Then, we show that W ฮป 0 pseudomonotone map is the same as a class of known pseudomonotone maps (Theorem 2) rather than its generalization (cf. [2] lines 2-3, p. 1260; lines 7-9, p. 1261). Besides, the relations between W ฮป 0 pseudomonotone map and L-generalized pseudomonotone map are discussed.

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## It is well known that monotonicity of a mapping implies its pseudomonotonicity. The purpose of this note is to study the situations under which pseudomonotonicity of a mapping implies its monotonicity. (~) 2004 Elsevier Ltd. All rights reserved.