### A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.

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Ky Fan’s minimax inequality [8, Theorem 1] has become a versatile tool in nonlinear and convex analysis. In this paper, we shall first obtain a minimax inequality which generalizes those generalizations of Ky Fan’s minimax inequality due to Allen [1], Yen [18], Tan [16], Bae Kim Tan [3] and Fan himself [9]. Several equivalent forms are then formulated and one of them, the maximal element version, is used to obtain a fixed point theorem which in turn is applied to obtain an existence theorem of an...

Using monotone bifunctions, we introduce a recession concept for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on variational problems. In the process we generalize some results by H. Brezis and H. Attouch relative to the convergence of the resolvents associated with maximal monotone operators.

The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor” between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted. In this...