Existence of Solutions for a New Class of GeneralizedQuasi-Equilibrium Problems in Hilbert Space

A new class of generalized equilibrium-like problems is studied in Hilbert space. By applying the FAN-KKM theorem, the existence and uniqueness of solutions of the auxiliary problem is found out, and some properties of the solution are obtained. Under suitable conditions, the solution and a common point for a non-expansive mapping of a mixed iterative sequence strongly convergent to generalized quasi-equilibrium problems are proven.