We introduce a Halpern-type iteration for a generalized mixed equilibrium problem in uniformly smooth and uniformly convex Banach spaces. Strong convergence theorems are also established in this paper. As applications, we apply our main result to mixed equilibrium, generalized equilibrium, and mixed variational inequality problems in Banach spaces. Finally, examples and numerical results are al...

Extending the characterization of the directional derivatives of a strongly regular solution to a variational inequality under parameter perturbations, this paper derives a first-order sensitivity result for a monotone-plus affine variational inequality (AVI) having non-isolated solutions. The result employs a “directional AVI” whose solutions provide the directional derivatives, if they exist,...

we introduce variational inequality problems on hilbert $c^*$-modules and we prove several existence results for variational inequalities defined on closed convex sets. then relation between variational inequalities, $c^*$-valued metric projection and fixed point theory  on  hilbert $c^*$-modules is studied.

As very powerful and important tools in the study of nonlinear sciences, variational inequalities and vector optimization have attracted so much attention. Over the last decades, variational inequality and vector optimization techniques have been applied extensively in such diverse fields as biology, chemistry, economics, engineering, game theory, management science, physics, and so on. The tho...

Variational inequality theory has become a rich source of inspiration in the pure and applied mathematics. Variational inequalities not only have stimulated new results dealing with nonlinear partial differential equations, but also have been used in a large variety of problems arising in mechanics, physics, optimization and control nonlinear programming, economics and transportation equilibriu...