Selected Papers from the 10th International Conference 2009 on Nonlinear Functional Analysis and Applications
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Citation: Journal of Inequalities and Applications 2011 2010:747463
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A General Iterative Method of Fixed Points for Mixed Equilibrium Problems and Variational Inclusion Problems
The purpose of this paper is to investigate the problem of finding a common element of the set of solutions for mixed equilibrium problems, the set of solutions of the variational inclusions with set-valued ma...
Citation: Journal of Inequalities and Applications 2010 2010:370197 -
Efficiency and Generalized Convex Duality for Nondifferentiable Multiobjective Programs
We introduce nondifferentiable multiobjective programming problems involving the support function of a compact convex set and linear functions. The concept of (properly) efficient solutions are presented. We f...
Citation: Journal of Inequalities and Applications 2010 2010:930457 -
Implicit Iteration Methods with Errors for Discrete Non-Lipschitzian Families with Perturbed Mappings
Motivated and inspired by the recent works on implicit iteration methods, we prove necessary and sufficient conditions for strong convergence of the eventually implicit iteration methods with errors to a commo...
Citation: Journal of Inequalities and Applications 2010 2010:820535 -
Contiguous Extensions of Dixon's Theorem on the Sum of a
In 1994, Lavoie et al. have succeeded in artificially constructing a formula consisting of twenty three interesting results, except for five cases, closely related to the classical Dixon's theorem on the sum o...
Citation: Journal of Inequalities and Applications 2010 2010:589618 -
Optimality Conditions and Duality in Nonsmooth Multiobjective Programs
We study nonsmooth multiobjective programming problems involving locally Lipschitz functions and support functions. Two types of Karush-Kuhn-Tucker optimality conditions with support functions are introduced. ...
Citation: Journal of Inequalities and Applications 2010 2010:939537 -
Optimality Conditions in Nondifferentiable G-Invex Multiobjective Programming
We consider a class of nondifferentiable multiobjective programs with inequality and equality constraints in which each component of the objective function contains a term involving the support function of a c...
Citation: Journal of Inequalities and Applications 2010 2010:172059 -
An Application of Category Theory to a Class of the Systems of the Superquadratic Wave Equations
We investigate the nontrivial solutions for a class of the systems of the superquadratic nonlinear wave equations with Dirichlet boundary condition and periodic condition with a superquadratic nonlinear terms ...
Citation: Journal of Inequalities and Applications 2010 2010:850602 -
Stability of Quadratic Functional Equations via the Fixed Point and Direct Method
Cădariu and Radu applied the fixed point theorem to prove the stability theorem of Cauchy and Jensen functional equations. In this paper, we prove the generalized Hyers-Ulam stability via the fixed point metho...
Citation: Journal of Inequalities and Applications 2010 2010:635720 -
Regularization Inertial Proximal Point Algorithm for Monotone Hemicontinuous Mapping and Inverse Strongly Monotone Mappings in Hilbert Spaces
The purpose of this paper is to present a regularization variant of the inertial proximal point algorithm for finding a common element of the set of solutions for a variational inequality problem involving a h...
Citation: Journal of Inequalities and Applications 2010 2010:451916 -
Approximation of Solutions to a System of Variational Inclusions in Banach Spaces
The purpose of this paper is to introduce an iterative method for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings. Strong convergence theorems are estab...
Citation: Journal of Inequalities and Applications 2010 2010:916806 -
-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations
We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop f...
Citation: Journal of Inequalities and Applications 2010 2010:895187 -
An Iterative Scheme with a Countable Family of Nonexpansive Mappings for Variational Inequality Problems in Hilbert Spaces
We introduce a new iterative scheme with a countable family of nonexpansive mappings for the variational inequality problems in Hilbert spaces and prove some strong convergence theorems for the proposed schemes.
Citation: Journal of Inequalities and Applications 2010 2010:687374 -
General Iterative Algorithm for Nonexpansive Semigroups and Variational Inequalities in Hilbert Spaces
We introduce a general iterative method for finding the solution of the variational inequality problem over the fixed point set of a nonexpansive semigroup in a Hilbert space. We prove that the sequence conver...
Citation: Journal of Inequalities and Applications 2010 2010:264052 -
Convergence Theorems on Generalized Equilibrium Problems and Fixed Point Problems with Applications
The purpose of this work is to introduce an iterative method for finding a common element of a solution set of a generalized equilibrium problem, of a solution set solutions of a variational inequality problem...
Citation: Journal of Inequalities and Applications 2010 2010:189036 -
Controllability for Variational Inequalities of Parabolic Type with Nonlinear Perturbation
We deal with the approximate controllability for the nonlinear functional differential equation governed by the variational inequality in Hilbert spaces and present a general theorems under which previous resu...
Citation: Journal of Inequalities and Applications 2010 2010:768469 -
Random Stability of an Additive-Quadratic-Quartic Functional Equation
Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation in ...
Citation: Journal of Inequalities and Applications 2010 2010:754210 -
Strong Convergence for Generalized Equilibrium Problems, Fixed Point Problems and Relaxed Cocoercive Variational Inequalities
We introduce a new iterative scheme for finding the common element of the set of solutions of the generalized equilibrium problems, the set of fixed points of an infinite family of nonexpansive mappings, and t...
Citation: Journal of Inequalities and Applications 2010 2010:728028 -
A Hybrid Iterative Scheme for Variational Inequality Problems for Finite Families of Relatively Weak Quasi-Nonexpansive Mappings
We consider a hybrid projection algorithm basing on the shrinking projection method for two families of relatively weak quasi-nonexpansive mappings. We establish strong convergence theorems for approximating t...
Citation: Journal of Inequalities and Applications 2010 2010:724851 -
Saddle Point Problems, Bilevel Problems, and Mathematical Program with Equilibrium Constraint on Complete Metric Spaces
We apply an existence theorem of variational inclusion problem on metric spaces to study optimization problems, set-valued vector saddle point problems, bilevel problems, and mathematical programs with equilib...
Citation: Journal of Inequalities and Applications 2010 2010:306403 -
Regularity for Solutions of Second-Order Nonlinear Integrodifferential Functional Equations
We deal with the well-posedness for solutions of nonlinear integrodifferential equations of second-order in Hilbert spaces by converting the problem into the contraction mapping principle with more general con...
Citation: Journal of Inequalities and Applications 2010 2010:280463 -
Stability of Approximate Quadratic Mappings
We investigate the general solution of the quadratic functional equation , in the class of all functions between quasi- ...
Citation: Journal of Inequalities and Applications 2010 2010:184542 -
Approximating Curve and Strong Convergence of the CQ Algorithm for the Split Feasibility Problem
Using the idea of Tikhonov's regularization, we present properties of the approximating curve for the split feasibility problem (SFP) and obtain the minimum-norm solution of SFP as the strong limit of the appr...
Citation: Journal of Inequalities and Applications 2010 2010:102085 -
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 class...
Citation: Journal of Inequalities and Applications 2010 2010:827082 -
Weak and Strong Convergence Theorems for Equilibrium Problems and Countable Strict Pseudocontractions Mappings in Hilbert Space
We introduce two iterative sequence for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a countable family of strict pseudocontractions in Hilbert Spac...
Citation: Journal of Inequalities and Applications 2010 2010:474813 -
Stability Criterion for Discrete-Time Systems
This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays. The problem is solved by applying a novel Lyapunov functional, a...
Citation: Journal of Inequalities and Applications 2010 2010:201459 -
Stability of a Cauchy-Jensen Functional Equation in Quasi-Banach Spaces
We obtain the generalized Hyers-Ulam stability of the Cauchy-Jensen functional equation .
Citation: Journal of Inequalities and Applications 2010 2010:151547 -
Generalized Bi-Quasivariational Inequalities for Quasi-Pseudomonotone Type II Operators on Noncompact Sets
We prove some existence results of solutions for a new class of generalized bi-quasivariational inequalities (GBQVI) for quasi-pseudomonotone type II and strongly quasi-pseudomonotone type II operators defined...
Citation: Journal of Inequalities and Applications 2010 2010:237191 -
Some Comparison Inequalities for Generalized Muirhead and Identric Means
For , with , the generalized Muirhead mean ...
Citation: Journal of Inequalities and Applications 2010 2010:295620 -
New Iterative Schemes for Asymptotically Quasi-Nonexpansive Mappings
We consider an iterative scheme for approximating the common fixed points of two asymptotically quasi-nonexpansive mappings in the intermediate sense in Banach spaces. The present results improve and extend so...
Citation: Journal of Inequalities and Applications 2010 2010:934692 -
On the Superstability of the Pexider Type Trigonometric Functional Equation
We will investigate the superstability of the (hyperbolic) trigonometric functional equation from the following functional equations: a...
Citation: Journal of Inequalities and Applications 2010 2010:897123 -
An Iterative Algorithm of Solution for Quadratic Minimization Problem in Hilbert Spaces
The purpose of this paper is to introduce an iterative algorithm for finding a solution of quadratic minimization problem in the set of fixed points of a nonexpansive mapping and to prove a strong convergence ...
Citation: Journal of Inequalities and Applications 2010 2010:717341 -
On the System of Nonlinear Mixed Implicit Equilibrium Problems in Hilbert Spaces
We use the Wiener-Hopf equations and the Yosida approximation notions to prove the existence theorem of a system of nonlinear mixed implicit equilibrium problems (SMIE) in Hilbert spaces. The algorithm for fin...
Citation: Journal of Inequalities and Applications 2010 2010:437976 -
Existence of Solutions for -Generalized Vector Variational-Like Inequalities
We introduce and study a class of -generalized vector variational-like inequalities and a class of ...
Citation: Journal of Inequalities and Applications 2010 2010:968271 -
Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces
The purpose of this paper is to use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi- ...
Citation: Journal of Inequalities and Applications 2010 2010:869684 -
Moudafi's Viscosity Approximations with Demi-Continuous and Strong Pseudo-Contractions for Non-Expansive Semigroups
We consider viscosity approximation methods with demi-continuous strong pseudo-contractions for a non-expansive semigroup. Strong convergence theorems of the purposed iterative process are established in the f...
Citation: Journal of Inequalities and Applications 2010 2010:645498 -
Superstability and Stability of the Pexiderized Multiplicative Functional Equation
We obtain the superstability of the Pexiderized multiplicative functional equation and investigate the stability of this equation in th...
Citation: Journal of Inequalities and Applications 2010 2010:486325 -
-Duality Theorems for Convex Semidefinite Optimization Problems with Conic Constraints
A convex semidefinite optimization problem with a conic constraint is considered. We formulate a Wolfe-type dual problem for the problem for its
Citation: Journal of Inequalities and Applications 2010 2010:363012 -
Fuzzy Stability of an Additive-Quadratic-Quartic Functional Equation
Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation:
Citation: Journal of Inequalities and Applications 2010 2010:253040 -
A New Iteration Method for Nonexpansive Mappings and Monotone Mappings in Hilbert Spaces
We introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings and monotone mappings in a Hilbert space. It is proved that the sequence generated by the iterative...
Citation: Journal of Inequalities and Applications 2010 2010:251761 -
Strong Convergence of an Implicit Iteration Process for a Finite Family of Uniformly -Lipschitzian Mappings in Banach Spaces
The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly -Lipschitzian mappings in Banach spa...
Citation: Journal of Inequalities and Applications 2010 2010:801961 -
Lyapunov Inequalities for One-Dimensional -Laplacian Problems with a Singular Weight Function
We estimate Lyapunov inequalities for a single equation, a cycled system and a coupled system of one-dimensional -Laplacian problems wit...
Citation: Journal of Inequalities and Applications 2009 2010:865096 -
Hyers-Ulam Stability of Differential Equation
We solve the inhomogeneous differential equation of the form , where
Citation: Journal of Inequalities and Applications 2009 2010:793197