Variational-Like Inequalities and Equilibrium Problems with Generalized Monotonicity in Banach Spaces. (13th December 2011) - Mahato Mahato, N. K. N. K.; Nahak Nahak, C. C.
Abstract : We introduce the notion of relaxed ( ρ - θ )- η -invariant pseudomonotone mappings, which is weaker than invariant pseudomonotone maps. Using the KKM technique, we establish the existence of solutions for variational-like inequality problems with relaxed ( ρ - θ )- η -invariant pseudomonotone mappings in reflexive Banach spaces. We also introduce the concept of ( ρ - θ )-pseudomonotonicity for bifunctions, and we consider some examples to show that ( ρ - θ )-pseudomonotonicity generalizes both monotonicity and strong pseudomonotonicity. The existence of solution for equilibrium problem with ( ρ - θ )-pseudomonotone mappings in reflexive Banach spaces are demonstrated by using the KKM technique.