We have obtained a new class of ordered pairs of multivalued maps that have pairs of coupled fixed points. We illustrate the main result with two examples that cover a wide range of models. We apply the main result in models in duopoly markets to get a market equilibrium and in aquatic ecosystems, also to get an equilibrium.

International audienc

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ABSTRACT. In this paper we study the local convergence of the methodin order to find the solution of the generalized equationWe first show that under the strong metric regularity of the linearization of the associated mapping and some additional assumptions regarding dependence on the parameter and the relation between the operator A and the Jacobian ∇ x f (p,x), we prove linear convergence of the method which is uniform in the parameter p. Then we go a step further and obtain a sequential implicit function theorem describing the dependence of the set of sequences of iterates of the parameter.

We generalize the notion of coupled fixed (or best proximity) points for cyclic ordered pairs of maps to p-cyclic ordered pairs of maps. We find sufficient conditions for the existence and uniqueness of the coupled fixed (or best proximity) points. We illustrate the results with an example that covers a wide class of maps.