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Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets

Mohammad Chowdhury, Kok-Keong Tan (2010)

Open Mathematics

In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s...

Generalized communication conditions and the eigenvalue problem for a monotone and homogenous function

Rolando Cavazos-Cadena (2010)

Kybernetika

This work is concerned with the eigenvalue problem for a monotone and homogenous self-mapping f of a finite dimensional positive cone. Paralleling the classical analysis of the (linear) Perron–Frobenius theorem, a verifiable communication condition is formulated in terms of the successive compositions of f , and under such a condition it is shown that the upper eigenspaces of f are bounded in the projective sense, a property that yields the existence of a nonlinear eigenvalue as well as the projective...

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