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Nonconvex minimization theorems for fixed point theorems in certain topological spaces. (English) Zbl 1084.47056

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.

MSC:

47J25 Iterative procedures involving nonlinear operators
47H05 Monotone operators and generalizations
47H10 Fixed-point theorems
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