Long orbit or empty valued principle, fixed point and surjectivity theorems (Q2822184)

Generalizing some results of the first author a flexible Long Orbit or Empty Value (LOEV) principle is proved in Theorem 2 of that paper. As first application of LOEV principle a Caristi-Kirk fixed-point theorem is shown in Theorem 4. The second part of this work is devoted to some surjectivity theorems. They are derived from a novel Theorem 8 which may be regarded as an interpolation between classical Groves theorem and a result of Ekeland from 2011. An Aubin derivative criterion for metric regularity of a continuous function is deduced from Theorem 8 in Theorem 10.