On \(\eta\)-upper sign property and upper sign continuity and their applications in equilibrium-like problems
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.
scientific article; zbMATH DE number 7021927