Zeqing Liu

Convergence of Iterative Sequences for Generalized Equilibrium Problems Involving Inverse-Strongly Monotone Mappings

The purpose of this paper is to consider the weak convergence of an iterative sequence for finding a common element in the set of solutions of generalized equilibrium problems, in the set of solutions of classical variational inequalities, and in the set of fixed points of nonexpansive mappings.

Sensitivity analysis for parametric completely generalized nonlinear implicit quasivariational inclusions

In this paper we introduce a new class of parametric completely generalized nonlinear implicit quasivariational inclusions and study the behavior and sensitivity analysis of the solution set of the parametric completely generalized nonlinear implicit quasivariational inclusion dealing with multivalued and single-valued nonlinear mappings in Hilbert spaces. Our results extend, improve and unify the previously many known results in this area.

Fixed point theorems for mappings satisfying contractive conditions of integral type and applications

In this paper, the existence, uniqueness and iterative approximations of fixed points for contractive mappings of integral type in complete metric spaces are established. As applications, the existence, uniqueness and iterative approximations of solutions for a class of functional equations arising in dynamic programming are discussed. The results presented in this paper extend and improve essentially the results of Branciari (A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29, 531-536, 2002), Kannan (Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76, 1968) and several known results. Four concrete examples involving the contractive mappings of integral type with uncountably many points are constructed.2010 Mathematics Subject Classfication: 54H25, 47H10, 49L20, 49L99, 90C39

General strongly nonlinear quasivariational inequalities with relaxed Lipschitz and relaxed monotone mappings

In this paper, we introduce and study a new class of general strongly nonlinear quasivariational inequalities and construct a general iterative algorithm by using the projection method. We establish the existence of a unique solution for general strongly nonlinear quasivariational inequalities involving relaxed Lipschitz, relaxed monotone, and strongly monotone mappings; we obtain the convergence and stability of the iterative sequences generated by the algorithm. Our results extend, improve, and unify many known results due to Bose, Noor, Siddiqi-Ansari, Verma, Yao, Zeng, and others.

On Properties of Solutions for a Class of Functional Equations Arising in Dynamic Programming

The existence, uniqueness, and iterative approximation of solutions for a class of functional equations arising in dynamic programming of multistage decision processes are discussed. Our results resolve in the affirmative an open problem posed in Ref. 1 and generalize important known results.

Convergence and stability of perturbed three-step iterative algorithm for completely generalized nonlinear quasivariational inequalities

In this paper, we introduce a new class of completely generalized nonlinear quasivariational inequalities and obtain its equivalence with a class of fixed point problems by using the resolvent operator technique. Using this equivalence, we develop perturbed three-step iterative algorithm for this class of completely generalized quasivariational inequalities. We establish a few existence theorems of unique solution for the class of completely generalized quasivariational inequalities involving relaxed monotone, generalized pseudocontractive and strongly monotone mappings and prove some convergence and stability results of iterative sequence generated by perturbed three-step iterative algorithm.

Properties of Solutions for Certain Functional Equations Arising in Dynamic Programming

AbstractIn this paper, we introduce and study properties of solutions for the following functional equation arising in dynamic programming of multistage decision processes

Stability of Ishikawa iteration methods with errors for strong pseudocontractions and nonlinear equations involving accretive operators in arbitrary Real Banach spaces

\eqalign{f(x) =\mathop{\hbox{opt}}\limits_{y \in D}\{u(x,y)\max\{p(x,y),f(a(x,y))\} +v(x,y)\min\{q(x,y),f(b(x,y))\}\cr +w(x,y)[r(x,y)+f(c(x,y))]\}, \quad \forall x\in{S}.}