
Minimax Theory and its Applications 09 (2024), No. 1, 143156 Copyright Heldermann Verlag 2024 Remarks on Fixed Point and Equilibrium Problems Wilfredo Sosa Economics Department, Catholic University of Brasilia, Brasil sosa@imca.edu.pe We consider the fixed point problem as two cases of the equilibrium problem in the sense of BlumOettli. 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. [ Fulltextpdf (130 KB)] for subscribers only. 