The existence theorems of solutions for generalized vector-valued variational-like inequalities

The purpose of this paper is to introduce a new kind of variational inequality, a ‘generalized vector variational-like inequality’ which includes several classical and well-known variational inequalities as special cases. As an application of the Knaster-Kuratowski-Mazurkiewicz principle as extended by Fan in 1961 [1], we prove that there exist solutions for our generalized vector variational-like inequality under reasonable hypotheses. These results generalize corresponding results given by Chen et al. in [2], Giannessi [3], Harker and Pang [4], Hartman and Stampacchia [5], Isac [6], Lee et al. [7], Noor [8], Saigal [9], Siddiqi et al. [10], and Yang [11].