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New versions on Nikaidô's coincidence theorem

Liang-Ju Chu, Ching-Yan Lin (2002)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In 1959, Nikaidô established a remarkable coincidence theorem in a compact Hausdorff topological space, to generalize and to give a unified treatment to the results of Gale regarding the existence of economic equilibrium and the theorems in game problems. The main purpose of the present paper is to deduce several generalized key results based on this very powerful result, together with some KKM property. Indeed, we shall simplify and reformulate a few coincidence theorems on acyclic multifunctions,...

Newton's methods for variational inclusions under conditioned Fréchet derivative

Ioannis K. Argyros, Saïd Hilout (2007)

Applicationes Mathematicae

Estimates of the radius of convergence of Newton's methods for variational inclusions in Banach spaces are investigated under a weak Lipschitz condition on the first Fréchet derivative. We establish the linear convergence of Newton's and of a variant of Newton methods using the concepts of pseudo-Lipschitz set-valued map and ω-conditioned Fréchet derivative or the center-Lipschitz condition introduced by the first author.

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