On \(\eta\)-upper sign property and upper sign continuity and their applications in equilibrium-like problems
type: Item
instance of: scholarly article
title: On \(\eta\)-upper sign property and upper sign continuity and their applications in equilibrium-like problems
zbMATH Open document ID: 1469.49011
DOI: 10.1155/2014/207502
author: A. Farajzadeh
author: Somaye Jafari
author: Chin-Tzong Pang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We first introduce the notion of \(\eta\)-upper sign property which is an extension of the upper sign property introduced in [\textit{M. Castellani} and \textit{M. Giuli}, J. Glob. Optim. 57, No. 4, 1213--1227 (2013; Zbl 1302.90249)], 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 [\textit{M. Bianchi} and \textit{R. Pini}, J. Optim. Theory Appl. 124, No. 1, 79--92 (2005; Zbl 1064.49004); Castellani and Giuli, loc. cit.; the first author and \textit{J. Zafarani}, Optimization 59, No. 3--4, 485--499 (2010; Zbl 1235.47060)]. Accordingly, it allows us to extend and obtain some existence results for equilibrium-like problems.
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 47J20
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 7021927
Wikidata QID: Q59036035
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/207502
OpenAlex ID: W1979620742
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description: scientific article; zbMATH DE number 7021927