Guest Editors: Qamrul Hasan Ansari, Suliman AlHomidan, and JenChih Yao
Equilibrium Problems and Fixed Point Theory

Citation: Fixed Point Theory and Applications 2012 2012:25

An Iteration Method for Common Solution of a System of Equilibrium Problems in Hilbert Spaces
The strong convergence theorem is proved for finding a common solution for a system of equilibrium problems: find where
Citation: Fixed Point Theory and Applications 2011 2011:780764 
Functions on Quasimetric Spaces and Fixed Points for Multivalued Maps
We discuss several properties of functions in the sense of AlHomidan et al.. In particular, we prove that the partial metric induced by any
Citation: Fixed Point Theory and Applications 2011 2011:603861 
New Iterative Scheme for Finite Families of Equilibrium, Variational Inequality, and Fixed Point Problems in Banach Spaces
We introduced a new iterative scheme for finding a common element in the set of common fixed points of a finite family of quasiÏ•nonexpansive mappings, the set of common solutions of a finite family of equilibri...
Citation: Fixed Point Theory and Applications 2011 2011:372975 
Strong Convergence Theorems by Shrinking Projection Methods for Class Mappings
We prove a strong convergence theorem by a shrinking projection method for the class of mappings. Using this theorem, we get a new resu...
Citation: Fixed Point Theory and Applications 2011 2011:681214 
A New Hybrid Algorithm for a System of Mixed Equilibrium Problems, Fixed Point Problems for Nonexpansive Semigroup, and Variational Inclusion Problem
The purpose of this paper is to consider a shrinking projection method for finding the common element of the set of common fixed points for nonexpansive semigroups, the set of common fixed points for an infini...
Citation: Fixed Point Theory and Applications 2011 2011:217407 
FixedPoint Results for Generalized Contractions on Ordered Gauge Spaces with Applications
The purpose of this paper is to present some fixedpoint results for singlevalued contractions on ordered and complete gauge space. Ou...
Citation: Fixed Point Theory and Applications 2011 2011:979586 
On the Existence Result for System of Generalized Strong Vector Quasiequilibrium Problems
We introduce a new type of the system of generalized strong vector quasiequilibrium problems with setvalued mappings in real locally convex Hausdorff topological vector spaces. We establish an existence theor...
Citation: Fixed Point Theory and Applications 2011 2011:475121 
Strong Convergence of Modified Halpern Iterations in CAT(0) Spaces
Strong convergence theorems are established for the modified Halpern iterations of nonexpansive mappings in CAT(0) spaces. Our results extend and improve the recent ones announced by Kim and Xu (2005), Hu (200...
Citation: Fixed Point Theory and Applications 2011 2011:869458 
Algorithms of Common Solutions to Generalized Mixed Equilibrium Problems and a System of Quasivariational Inclusions for Two Difference Nonlinear Operators in Banach Spaces
We consider a new iterative algorithm for finding a common element of the set of generalized mixed equilibrium problems, the set of solutions of a system of quasivariational inclusions for two difference inver...
Citation: Fixed Point Theory and Applications 2011 2011:601910 
Convergence Analysis for a System of Generalized Equilibrium Problems and a Countable Family of Strict Pseudocontractions
We introduce a new iterative algorithm for a system of generalized equilibrium problems and a countable family of strict pseudocontractions in Hilbert spaces. We then prove that the sequence generated by the p...
Citation: Fixed Point Theory and Applications 2011 2011:941090 
VariationalLike Inclusions and Resolvent Equations Involving Infinite Family of SetValued Mappings
We study variationallike inclusions involving infinite family of setvalued mappings and their equivalence with resolvent equations. It is established that variationallike inclusions in real Banach spaces ar...
Citation: Fixed Point Theory and Applications 2010 2011:635030 
Optimal Solutions in Nonconvex SemiInfinite Programs with Support Functions
Approximate optimality conditions for a class of nonconvex semiinfinite programs involving support functions are given. The objective function and the constraint functions are locally Lipschitz functions on
Citation: Fixed Point Theory and Applications 2010 2011:175327 
Strong Convergence of an Implicit Algorithm in CAT(0) Spaces
We establish strong convergence of an implicit algorithm to a common fixed point of a finite family of generalized asymptotically quasinonexpansive maps in CAT ...
Citation: Fixed Point Theory and Applications 2010 2011:173621 
Fixed Point Theorems for Monotone Mappings on Partial Metric Spaces
Matthews (1994) introduced a new distance on a nonempty set
Citation: Fixed Point Theory and Applications 2010 2011:508730 
General Viscosity Approximation Methods for Common Fixed Points of Nonexpansive Semigroups in Hilbert Spaces
This paper is devoted to the strong convergence of two kinds of general viscosity iteration processes for approximating common fixed points of a nonexpansive semigroup in Hilbert spaces. The results presented ...
Citation: Fixed Point Theory and Applications 2010 2011:783502 
Hamming StarConvexity Packing in Information Storage
A major puzzle in neural networks is understanding the information encoding principles that implement the functions of the brain systems. Population coding in neurons and plastic changes in synapses are two im...
Citation: Fixed Point Theory and Applications 2010 2011:615274 
Hybrid Algorithm for Finding Common Elements of the Set of Generalized Equilibrium Problems and the Set of Fixed Point Problems of Strictly Pseudocontractive Mapping
The purpose of this paper is to prove the strong convergence theorem for finding a common element of the set of fixed point problems of strictly pseudocontractive mapping in Hilbert spaces and two sets of gene...
Citation: Fixed Point Theory and Applications 2010 2011:274820 
A Generalized Hybrid SteepestDescent Method for Variational Inequalities in Banach Spaces
The hybrid steepestdescent method introduced by Yamada (2001) is an algorithmic solution to the variational inequality problem over the fixed point set of nonlinear mapping and applicable to a broad range of ...
Citation: Fixed Point Theory and Applications 2010 2011:754702 
Critical Point Theorems and Ekeland Type Variational Principle with Applications
We introduce the notion of spaces which is much weaker than cone metric spaces defined by Huang and X. Zhang (2007). We establish some ...
Citation: Fixed Point Theory and Applications 2010 2011:914624 
System of General Variational Inequalities Involving Different Nonlinear Operators Related to Fixed Point Problems and Its Applications
By using the projection methods, we suggest and analyze the iterative schemes for finding the approximation solvability of a system of general variational inequalities involving different nonlinear operators i...
Citation: Fixed Point Theory and Applications 2010 2011:689478 
The Existence of Maximum and Minimum Solutions to General Variational Inequalities in the Hilbert Lattices
We apply the variational characterization of the metric projection to prove some results about the solvability of general variational inequalities and the existence of maximum and minimum solutions to some gen...
Citation: Fixed Point Theory and Applications 2010 2011:904320 
Iterative Methods for Family of Strictly Pseudocontractive Mappings and System of Generalized Mixed Equilibrium Problems and Variational Inequality Problems
We introduce a new iterative scheme by hybrid method for finding a common element of the set of common fixed points of infinite family of
Citation: Fixed Point Theory and Applications 2010 2011:852789 
Solving the Set Equilibrium Problems
We study the weak solutions and strong solutions of set equilibrium problems in real Hausdorff topological vector space settings. Several new results of existence for the weak solutions and strong solutions of...
Citation: Fixed Point Theory and Applications 2010 2011:945413 
Strong Convergence of a New Iterative Method for Infinite Family of Generalized Equilibrium and FixedPoint Problems of Nonexpansive Mappings in Hilbert Spaces
We introduce an iterative algorithm for finding a common element of the set of solutions of an infinite family of equilibrium problems and the set of fixed points of a finite family of nonexpansive mappings in...
Citation: Fixed Point Theory and Applications 2010 2011:392741 
Relation between Fixed Point and Asymptotical Center of Nonexpansive Maps
We introduce the concept of asymptotic center of maps and consider relation between asymptotic center and fixed point of nonexpansive maps in a Banach space.
Citation: Fixed Point Theory and Applications 2010 2011:175989 
A HybridExtragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone Mappings
We introduce a new iterative scheme based on both hybrid method and extragradient method for finding a common element of the solutions set of a system of equilibrium problems, the fixed points set of a nonexpa...
Citation: Fixed Point Theory and Applications 2010 2011:232163 
New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces
We introduce new general iterative approximation methods for finding a common fixed point of a countable family of nonexpansive mappings. Strong convergence theorems are established in the framework of reflexi...
Citation: Fixed Point Theory and Applications 2010 2011:671754 
A General Iterative Approach to Variational Inequality Problems and Optimization Problems
We introduce a new general iterative scheme for finding a common element of the set of solutions of variational inequality problem for an inversestrongly monotone mapping and the set of fixed points of a none...
Citation: Fixed Point Theory and Applications 2010 2011:284363 
An Implicit Extragradient Method for Hierarchical Variational Inequalities
As a wellknown numerical method, the extragradient method solves numerically the variational inequality of finding
Citation: Fixed Point Theory and Applications 2010 2011:697248 
Iterative Algorithms for Finding Common Solutions to Variational Inclusion Equilibrium and Fixed Point Problems
The main purpose of this paper is to introduce an explicit iterative algorithm to study the existence problem and the approximation problem of solution to the quadratic minimization problem. Under suitable con...
Citation: Fixed Point Theory and Applications 2010 2011:915629 
Quasigauge Spaces with Generalized Quasipseudodistances and Periodic Points of Dissipative SetValued Dynamic Systems
In quasigauge spaces, we introduce the families of generalized quasipseudodistances, and we define three kinds of dissipative setvalued dynamic systems with these families of generalized quasipseudodistances...
Citation: Fixed Point Theory and Applications 2010 2011:712706 
Iterative Methods for Variational Inequalities over the Intersection of the Fixed Points Set of a Nonexpansive Semigroup in Banach Spaces
This paper presents a framework of iterative methods for finding specific common fixed points of a nonexpansive selfmappings semigroup in a Banach space. We prove, with appropriate conditions, the strong conv...
Citation: Fixed Point Theory and Applications 2010 2011:620284 
Hybrid ProximalType Algorithms for Generalized Equilibrium Problems, Maximal Monotone Operators, and Relatively Nonexpansive Mappings
The purpose of this paper is to introduce and consider new hybrid proximaltype algorithms for finding a common element of the set of solutions...
Citation: Fixed Point Theory and Applications 2010 2011:973028 
A Viscosity of CesÃ ro Mean Approximation Methods for a Mixed Equilibrium, Variational Inequalities, and Fixed Point Problems
We introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a ...
Citation: Fixed Point Theory and Applications 2010 2011:945051 
Fixed Point Results in Quasimetric Spaces
In the setting of quasimetric spaces, we prove some new results on the existence of fixed points for contractive type maps with respect to
Citation: Fixed Point Theory and Applications 2010 2011:178306 
Iterative Approaches to Find Zeros of Maximal Monotone Operators by Hybrid Approximate Proximal Point Methods
The purpose of this paper is to introduce and investigate two kinds of iterative algorithms for the problem of finding zeros of maximal monotone operators. Weak and strong convergence theorems are established ...
Citation: Fixed Point Theory and Applications 2010 2011:282171 
Coupled Coincidence Point Theorems for Nonlinear Contractions in Partially Ordered QuasiMetric Spaces with a QFunction
Using the concept of a mixed gmonotone mapping, we prove some coupled coincidence and coupled common fixed point theorems for nonlinear contractive mappings in partially ordered complete quasimetric spaces with...
Citation: Fixed Point Theory and Applications 2010 2011:703938