A Combined Feasible-Nonfeasible Point Continuation Method for Strongly Monotone Variational Inequalities

In this paper, we discuss the variational inequality problems VIP(X, F), where Fis a strongly monotone function and the convex feasible set X is described by some inequality eonstraints. We present a continuation method for VIP(X. F). which solves a sequence ofperturbed variational inequality problems PVIP(X. F, ε. μ) depending on two parameters ε≥ 0and μ＞0. It is worthy to point out that the method will be a feasible point type whenε = 0 and a nonfeasible point type when ε＞0, i.e., it is a combined feasible-nonfeasible point(CFNFP for short) method. We analyse the existence, uniqueness and continuity of the solutionto PVIP(X, F, ε,μ), and prove that any sequence generated by this method converges to theunique solution of VIP(X, F).

A Note on Equilibrium of Eventually Strongly Monotone Skew-product Semiflows

In this paper, we show that for an eventually strongly monotone skew-product semiflow τ, the strict ordering on Ec （the set consisting of continuous equilibria of τ） implies the strong one.

SOME PROPERTIES OF STRONGLY MONOTONICALLY T2 SPACES

This paper investigates Buck＇s question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having a cushioned pair-base space and compact strongly monotonically T2 space,some results （Theorems 1--3） are obtained.

A SOLUTION OF A GENERAL EQUILIBRIUM PROBLEM

Under the framework of a real Hilbert space, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem and the set of fixed points of a nonexpansive semigroup. Moreover, a numerical example is presented. This example grantee the main result of the paper.

Hybrid projection method for generalized mixed equilibrium problems,variational inequality problems,and fixed point problems in Banach spaces

A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.

EXISTENCE AND ITERATIVE ALGORITHMS OF SOLUTIONS FOR GENERALIZED MIXED QUASI_VARIATIONAL INEQUALITIES

In this paper, by using the auxiliary technique of variational inequalities, the existence and iterative algorithm; of solutions for a class of generalized mixed quasi-variational inequalities are studied. Our results answer the open problems mentioned by Noor, improve and generalize some recent known results.

PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS

A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings

Iterative algorithm of solutions for multivalued general mixed implicit equilibrium-like problems

The multivalued general mixed implicit equilibrium-like problems are introduced and studied. To solve these problems, a new predictor-corrector iterative algorithm is proposed and analyzed using the auxiliary principle technique. The convergence of the suggested algorithm is also proved in weaker conditions.

General Convergence Analysis for Three-step Projection Methods and Applications to Variational Problems

First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.

Iterative Algorithms of Common Solutions for Quasi-Variational Inclusion and Fixed Point Problems

By introducing the resolvent operator associated with a maximal monotone mapping, the author obtains a strong convergence theorem of a generalized iterative algorithm for a class of quasi-variational inclusion problems, which extends and unifies some recent results.

A Weak Convergence Theorem for Equilibrium Problems,Variational Inequalities and Fixed Point Problems in 2-Uniformly Convex Banach Spaces

In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem,the set of solutions of variational inequalities for an α-inversely strongly monotone operator and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and 2-uniformly convex Banach space.Some weak convergence theorems are obtained,to extend the previous work.