Topological fixed point theory and applications to variational inequalities

Fixed-Point Theory, Variational Inequalities, and Its Approximation Algorithms

Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems

and Applied Analysis 3 for all x, y ∈ C. A mapping A : C → H is said to be α-inverse strongly g-monotone if and only if 〈 Ax −Ay, g x − gy ≥ α∥Ax −Ay∥2, 2.2 for some α > 0 and for all x, y ∈ C. A mapping g : C → C is said to be strongly monotone if there exists a constant γ > 0 such that 〈 g x − gy, x − y ≥ γ∥x − y∥2, 2.3 for all x, y ∈ C. Let B be a mapping ofH into 2 . The effective domain of...

Explicit Hierarchical Fixed Point Approach to Variational Inequalities

Abstract: An explicit hierarchical fixed point algorithm is introduced to solve monotone variational inequalities, which are governed by a pair of nonexpansive mappings, one of which is used to define the governing operator and the other to define the feasible set. These kinds of variational inequalities include monotone inclusions and convex optimization problems to be solved over the fixed po...

Theory and Applications of Variational Inequalities

Monotone variational inequalities, generalized equilibrium problems and fixed point methods

In this paper, we study monotone variational inequalities and generalized equilibrium problems. Weak convergence theorems are established based on a fixed point method in the framework of Hilbert spaces.