A note on the combination of equilibrium problems

Nguyen Thi Thanh Ha (), Tran Thi Huyen Thanh (), Nguyen Ngoc Hai (), Hy Duc Manh () and Bui Dinh ()
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Nguyen Thi Thanh Ha: Le Quy Don Technical University
Tran Thi Huyen Thanh: Le Quy Don Technical University
Nguyen Ngoc Hai: Trade Union University
Hy Duc Manh: Le Quy Don Technical University
Bui Dinh: Le Quy Don Technical University

Mathematical Methods of Operations Research, 2020, vol. 91, issue 2, No 6, 323 pages

Abstract: Abstract We show that the solution set of a strictly convex combination of equilibrium problems is not necessarily contained in the corresponding intersection of solution sets of equilibrium problems even if the bifunctions defining the equilibrium problems are continuous and monotone. As a consequence, we show that some results given in some recent papers are not always true. Therefore different numerical methods for computing common solutions of families of equilibrium problems proposed in the literature may not converge under the monotonicity assumption. Finally, we prove that if the bifunctions are also parapseudomonotone, then the solution set of any strictly convex combination of a family of equilibrium problems is equivalent to the solution set of the intersection of the same family of equilibrium problems.

Keywords: Equilibria; Ky Fan inequality; Combination of equilibrium problems; 47H10; 49J40; 49J52; 90C30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00186-019-00690-w

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