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Nirenberg-type problems in Banach lattices

Duma A., Duma I.

Journal of Applied Analysis

2010

Vol. 16, nr 2

189-197

A slightly modified version of the celebrated Nirenberg problem concerning expanding maps is considered. A positive answer is given for a type of lattice-expansive operators in discrete Hilbert lattices. Our approach is motivated by the study of the infinite systems of nonlinear equations.

Generalized multivalued contractions which are quasi-bounded

Petrusel G.

Demonstratio Mathematica

2007

Vol. 40, nr 3

639-648

The purpose of this note is to study the following problem: which multi- valued generalized contractions are quasi-bounded with the quasi-norm strictly less than 1 ? As consequences, some surjectivity results are given.