Lucas Fresse1 , Viorica V. Motreanu2
Abstract. We establish sufficient conditions for the existence of nonlinear error bounds for submonotone maps defined on a pseudometric space endowed with a preorder. This covers the case of submonotone maps (thus a fortiori of lower semicontinuous maps) on a metric space (endowed with the trivial preorder). In particular our results generalize the existing results for this case. Our arguments are based on an appropriate version of Ekeland’s variational principle.
Keywords: nonlinear error bound, pseudometric space, preorder, submonotone map, variational principle.
MSC: 49J52, 58E30, 06A75.
DOI 10.56082/annalsarscimath.2025.1.169
1 Universite de Lorraine, Institut Elie Cartan, 54506 Vandoeuvre-les-Nancy, France, lucas.fresse@univ-lorraine.fr
2 Lycee Varoquaux, 10 rue Jean Moulin, 54510 Tomblaine, France, vmotreanu@gmail.com
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 17 no 1, 2025
