Jung, Jong Soo; Cho, Yeol Je; Kang, Shin Min Nonconvex minimization theorems for fixed point theorems in certain topological spaces. (English) Zbl 1084.47056 Panam. Math. J. 15, No. 2, 67-77 (2005). The authors establish a new nonconvex minimization theorem by using a family of weak quasi-metrics, and improve the Downing-Kirk fixed point theorem. They also obtain a formally stronger form of the Ekeland \(\varepsilon\)-variational principle in the same space. Reviewer: Ji-Cheng Hou (Beijing) MSC: 47J25 Iterative procedures involving nonlinear operators 47H05 Monotone operators and generalizations 47H10 Fixed-point theorems Keywords:nonconvex minimization; family of weak quasimetrics; Downing-Kirk fixed point theorem; Caristi fixed point theorem; Ekeland variational principle PDFBibTeX XMLCite \textit{J. S. Jung} et al., Panam. Math. J. 15, No. 2, 67--77 (2005; Zbl 1084.47056)