On some generalizations of Ekeland’s principle and inward contractions in gauge spaces

Research paper by M. Frigon

Indexed on: 12 Nov '11Published on: 12 Nov '11Published in: Journal of Fixed Point Theory and Applications


We give generalizations in complete gauge spaces of the following results: Bishop-Phelps’ theorem, Ekeland’s variational principle, Caristi’s fixed point theorem, the drop theorem and the flower petal theorem. We show that our generalizations are equivalent. We apply those results to obtain fixed point theorems for multivalued contractions defined on a closed subset of a complete gauge space and satisfying a generalized inwardness condition.