Some existence results of efficiency in vector optimization

This paper presents several new results concerning the existence of efficient solutions for vector maximization problems. First, an improved version of the Caristi–Kirk fixed point theorem is obtained. This theorem is then used to derive two existence results for vector maximization which generalize some results of G. Isac. Second, another result of Isac is generalized to the vector case to yield an additional existence result for vector maximization problems. Finally, the concept of nuclear cones is extended from scalar to vector form. This is used to derive another existence theorem for efficient points of vector maximization problems.