Vectorial Ekeland Variational Principles and Inclusion Problems in Cone Quasi-Uniform Spaces

Abstract

Some new vectorial Ekeland variational principles in conequasi-uniform spaces are proved. Some new equivalent principles, vectorialquasivariational inclusion principle, vectorial quasi-optimizationprinciple, vectorial quasiequilibrium principle are obtained. Also, severalother important principles in nonlinear analysis are extended to conequasi-uniform spaces. The results of this paper extend, generalize, andimprove the corresponding results for Ekeland's variational principles ofthe directed vectorial perturbation type and other generalizations ofEkeland's variational principles in the setting of $F$-type topologicalspace and quasi-metric spaces in the literatures. Even in usual real metricspaces, some of our results are new.