We present two proximal algorithms for solving the mixed equilibrium problems. Under some simpler framework, the strong and weak convergence of the sequences defined by two general algorithms is respectively obtained. In particular, we deal with several iterative schemes in a united way and apply our algorithms for solving the classical equilibrium problem, the minimization problem, the classic...

A zero of a piecewise smooth function f is said to be nondegenerate if the function is Fr echet diierentiable at that point. Using this concept, we describe the usual nondegeneracy notions in the settings of nonlinear (vertical, horizontal, mixed) complementarity problems and the variational inequality problem corresponding to a polyhedral convex set. Some properties of nondegenerate zeros of p...

We analyze the nite element method for a class of mixed variational inequalities of the second kind, which arises in elastoplastic problems. An abstract variational inequality, of which the elastoplastic problems are special cases, has been previously introduced and analyzed 31], and existence and uniqueness results for this problem have been given there. In this contribution the same approach ...

This paper introduces new mixed vector FQ-implicit variational inequality problems and corresponding mixed vector FQ-implicit complementarity problems for set-valued mappings, and studies the equivalence between them under certain assumptions in Banach spaces. It also derives some new existence theorems of solutions for them with examples under suitable assumptions without monotonicity. This pa...

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.

This paper deals with the abstract generalized vector quasi-equilibrium problem in noncompact Hadamard manifolds. We prove the existence of solutions to the abstract generalized vector quasi-equilibrium problem under suitable conditions and provide applications to an abstract vector quasi-equilibrium problem, a generalized scalar equilibrium problem, a scalar equilibrium problem, and a perturbe...

In this paper, a new concept of -proximal mapping for a proper subdifferentiable functional (which may not be convex) on a Banach space is introduced. An existence and Lipschitz continuity of the -proximal mapping are proved. By using properties of the -proximal mapping, a new class of general mixed variational inequalities is introduced and studied in Banach spaces. An existence theorem of sol...

By applying the concept of partially relaxed -strong monotonicity of set-valued mappings due to author and the auxiliary variational inequality technique, some new predictor–corrector iterative algorithms for solving generalized mixed quasi-variational-like inclusions are suggested and analyzed. The convergence of the algorithms only need the continuity and the partially relaxed -stronglymonoto...