Vector variational-like inequalities with relaxed η-α pseudomonotone mappings in Banach spaces
Keqing Wu, Nan‐jing Huang · Journal of Mathematical Inequalities · 2007
In this paper, we introduce two new concepts of relaxed - pseudomonotonicity and relaxed - demipseudomonotonicity as well as two classes of vector variational-like inequalities with relaxed - peseudomonotone mappings and relaxed - demipseudomonotone mappings in Banach spaces. By using KKM technique, we obtain the existence of solutions for vector variational-like inequalities with relaxed - pseudomonotone mappings in reflexive Banach spaces. We also show the solvability of vector variational-like inequalities with relaxed - demipseudomonotone mappings in reflexive Banach spaces by means of Kakutani-Fan-Glicksberg fixed-point theorem. The results presented in this paper extend and improve some corresponding results of several authors.