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

Some new vectorial Ekeland variational principles in cone quasi‐uniform spaces are proved. Some new equivalent principles, vectorial quasivariational inclusion principle, vectorial quasi‐optimization principle, vectorial quasiequilibrium principle are obtained. Also, several other important principles in nonlinear analysis are extended to cone quasi‐uniform spaces. The results of this paper extend, generalize, and improve the corresponding results for Ekeland′s variational principles of the directed vectorial perturbation type and other generalizations of Ekeland′s variational principles in the setting of F‐type topological space and quasi‐metric spaces in the literatures. Even in usual real metric spaces, some of our results are new.