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    STUDIA MATHEMATICA - Issue no. 1 / 2022  
         
  Article:   WELL-POSEDNESS FOR SET-VALUED EQUILIBRIUM PROBLEMS.

Authors:  MIHAELA MIHOLCA.
 
       
         
  Abstract:  
DOI: 10.24193/subbmath.2022.1.07

Published Online: 2022-03-10
Published Print: 2022-03-31
pp. 91-103

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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.

Keywords: Set-valued equilibrium problems, well-posedness, maximizing sequences, minimizing sequences.

Mathematics Subject Classification (2010): 49J53, 49K40.
 
         
     
         
         
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