A selection theorem is proved which contains as a particular case results of N. C. Yannelis
and N. D. Prabhakar
[J. Math. Econ. 12, 233-245 (1983; Zbl 0536.90019
)] and of X. P. Ding, W. K. Kim, K.-K. Tan
[Bull. Aust. Math. Soc. 46, 205-212 (1992; Zbl 0762.47030
)]. Applying this selection, a fixed point theorem, a nonempty intersection theorem, some existence theorems of solutions for generalized quasi-variational inequalities and some equilibrium existence theorems for abstract economies are proved.