On η-Upper Sign Property and Upper Sign Continuity and Their Applications in Equilibrium-Like Problems

We first introduce the notion of η -upper sign propertywhich is an extension of the upper sign property introduced in Castellani and Giuli, 2013, by relaxing convexity on the set. Afterwards, we establish a link between the solution sets of local dual equilibrium problem (Minty local equilibrium pro...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.894-899-195
Main Authors: Farajzadeh, Ali, Pang, Chin-Tzong, Jafari, Somaye
Format: Article
Language:English
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Summary:We first introduce the notion of η -upper sign propertywhich is an extension of the upper sign property introduced in Castellani and Giuli, 2013, by relaxing convexity on the set. Afterwards, we establish a link between the solution sets of local dual equilibrium problem (Minty local equilibrium problem) and equilibrium problem for mappings whose domains are not necessarily convex by relaxing the upper sign continuity on the map, as it is assumed in the literature (Bianchi and Pini, 2005; Castellani and Giuli, 2013; Farajzadeh and Zafarani, 2010). Accordingly, it allows us to extend and obtain some existence results for equilibrium-like problems.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/207502