Well-posedness for set-valued equilibrium problems - MIHOLCA, Mihaela (Studia Universitatis Babeș-Bolyai Mathematica, 2022)
In this paper we extend a concept of well-posedness for vector equilibrium problems to the more general framework of set-valued equilibrium problems in topological vector spaces using an appropriate reformulation of the concept of minimality for sets. Sufficient conditions for well-posedness are given in the generalized convex settings and we are able to single out classes of well-posed set-valued equilibrium problems. On the other hand, in order to relax some conditions, we introduce a concept of minimizing sequences for a set-valued problem, in the set criterion sense, and further we will have a concept of well-posedness for the set-valued equilibrium problem we are interested in. Sufficient results are also given for this well-posedness concept. Mathematics Subject Classification (2010): 49J53, 49K40. Received 05 December 2021; Revised 21 January 2022; Accepted 01 February 2022.