On η -Upper Sign Property and Upper Sign Continuity and Their Applications in Equilibrium-Like Problems
Ali P. Farajzadeh, Somaye Jafari, Chin-Tzong Pang · Abstract and Applied Analysis · 2014
We first introduce the notion of η -upper sign property which 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.