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Equilibrium problems in Hadamard manifolds. (English) Zbl 1273.49015

Summary: An equilibrium theory is developed in Hadamard manifolds. The existence of equilibrium points for a bifunction is proved under suitable conditions, and applications to variational inequality, fixed point and Nash equilibrium problems are provided. The convergence of the Picard iteration for firmly nonexpansive mappings along with the definition of resolvents for bifunctions in this setting is used to devise an algorithm to approximate equilibrium points.

MSC:

49J40 Variational inequalities
49J99 Existence theories in calculus of variations and optimal control
53C20 Global Riemannian geometry, including pinching
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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