Ekeland variational principle in complete weakly symmetric (1, q2)-quasimetric spaces and applications. (4th May 2023) - Yang, Hongzhen; Li, Jun
Abstract : In this paper, Ekeland variational principle for bifunctions is given in complete weakly symmetric ( 1, q 2 ) -quasimetric spaces and it is shown to be equivalent to Oettli–Théra theorem, Caristi–Kirk fixed point theorem and Takahashi's nonconvex minimization principle. Moreover, Ekeland variational principle for the system of bifunctions is obtained. Finally, by applying obtained results, the existence of solutions of quasi-equilibrium problems (QEP) and uncountable system of QEP is provided under the compactness condition and the generalized Caristi-like condition, respectively.