Zili Wu - Academia.edu (original) (raw)
Related Authors
King AbdulAziz University (KAU) Jeddah, Saudi Arabia
Uploads
Papers by Zili Wu
Nonlinear Analysis: Theory, Methods & Applications, 2003
We prove that for some 0 ¡ and 0 ¡ 6 + ∞ a proper lower semicontinuous and bounded below function... more We prove that for some 0 ¡ and 0 ¡ 6 + ∞ a proper lower semicontinuous and bounded below function f on a metric space (X; d) satisÿes that for each x ∈ X with inf X f ¡ f(x) ¡ inf X f + there exists y ∈ X such that 0 ¡ d(x; y) 6 f(x) − f(y) i for each such x this inequality holds for some minimizer z of f. Similar conditions are shown to be su cient for f to possess minimizers, weak sharp minima and error bounds. A ÿxed point theorem is also established. Moreover, these results all turn out to be equivalent to the Ekeland variational principle, the Caristi-Kirk ÿxed point theorem and the Takahashi theorem.
Nonlinear Analysis: Theory, Methods & Applications, 2003
We prove that for some 0 ¡ and 0 ¡ 6 + ∞ a proper lower semicontinuous and bounded below function... more We prove that for some 0 ¡ and 0 ¡ 6 + ∞ a proper lower semicontinuous and bounded below function f on a metric space (X; d) satisÿes that for each x ∈ X with inf X f ¡ f(x) ¡ inf X f + there exists y ∈ X such that 0 ¡ d(x; y) 6 f(x) − f(y) i for each such x this inequality holds for some minimizer z of f. Similar conditions are shown to be su cient for f to possess minimizers, weak sharp minima and error bounds. A ÿxed point theorem is also established. Moreover, these results all turn out to be equivalent to the Ekeland variational principle, the Caristi-Kirk ÿxed point theorem and the Takahashi theorem.