A generalization of Caristi’s theorem with applications to nonlinear mapping theory
A generalization of Caristi’s theorem with applications to nonlinear mapping theory
Suppose X and Y are complete metric spaces, g: X-+X an arbitrary mapping:, and f:X->Y a closed mapping (thus, for {xJczX the conditions x n -+x and f(x n )->y imply f(x) = y).It is shown that if there exists a lower semicontinuous function φ mapping f(X) into the nonnegative …