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Minimax Theory and its Applications 09 (2024), No. 1, 143--156
Copyright Heldermann Verlag 2024

Remarks on Fixed Point and Equilibrium Problems

Wilfredo Sosa
Economics Department, Catholic University of Brasilia, Brasil

We consider the fixed point problem as two cases of the equilibrium problem in the sense of Blum-Oettli. The first case explores the properties of maximal σ monotone operators, to propose necessary and sufficient conditions to guarantee the existence of fixed points. The second case transforms the fixed point problem, defined by an operator that has closed images not necessarily σ monotone, into an equilibrium problem, with a different approach than the first case. Also, we establish a methodology to extend any σ (with function σ bounded) monotone operator into a maximal σ monotone operator.

Keywords: Fixed point problem, equilibrium problem, sigma monotone operator.

MSC: 47N10, 47H04, 47H10.

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