In this paper, we present several existence results for efficient solutions
and efficient points in vector optimization problems. Firstly, we apply a
corollary of a recently obtained Caristi-Kirk fixed point theorem ([3]) to
obtain existence results for efficient solutions of a vector optimization p
roblem, which generalize the existence theorems of efficient solutions in [
2] (Theorem 9 and its Corollary). Secondly, we generalize Theorem 10 in [2]
to the vector case, obtaining an existence result for efficient points of
a vector optimization problem. As a result, an open problem following the C
orollary of Theorem 10 in [2] is solved in some way. Finally, the concept o
f nuclear cones introduced in [5] is extended, somehow answering another op
en question in [2] (in the Remark following the Corollary of Theorem 9). Ap
plying this concept of generalized nuclear cones, we derive another existen
ce theorem of efficient points.