Equations with discontinuous nonlinear semimonotone operators

summary:The aim of this paper is to present an existence theorem for the operator equation of Hammerstein type $x+KF(x)=0$ with the discontinuous semimonotone operator $F$. Then the result is used to prove the existence of solution of the equations of Urysohn type. Some examples in the theory of nonlinear equations in $L_p(\Omega )$ are given for illustration

A New Iterative Method for the Set of Solutions of Equilibrium Problems and of Operator Equations with Inverse-Strongly Monotone Mappings

The purpose of the paper is to present a new iteration method for finding a common element for the set of solutions of equilibrium problems and of operator equations with a finite family of λi-inverse-strongly monotone mappings in Hilbert spaces

Convergence rates and finite-dimensional approximation for a class of ill-posed variational inequalities

The purpose of this paper is to investigate an operator version of Tikhonov regularization for a class of ill-posed variational inequalities under arbitrary perturbation operators. Aspects of convergence rate and finite-dimensional approximations are considered. An example in the theory of generalized eigenvectors is given for illustration

Inertial proximal point regularization algorithm for unconstrained vector convex optimization problems

The purpose of the paper is to investigate an iterative regularization method of proximal point type for solving ill-posed vector convex optimization problems in Hilbert spaces. The application to the convex feasibility problems and the common fixed points for nonexpansive potential mappings is also given.Досліджено ітеративний метод регуляризації типу проксимальної точки для розв'язку некоректних векторних опуклих задач оптимізації у гільбертових просторах. Наведено також застосування методу до задач опуклої припустимості та до задачі про спільні нерухомі точки для нерозширних відображень потенціала

Discrepancy Principle and Convergence Rates in Regularization of Monotone Ill-Posed Problems

The convergence rates of the regularized solution as well as its Galerkin approximations for nonlinear monotone ill-posed problems in a Banach space are established on the basis of the choice of a regularization parameter by the Morozov discrepancy principle.На основі вибору параметра регуляризації відповідно до принципу нев'язки Морозова встановлено швидкості збіжності як регуляризованих розв'язків нелінійних монотонних некоректних задач у банаховому просторі, так і їх наближень Гальоркіна

Regularization for a Common Solution of a System of Nonlinear Ill-Posed Equations

Abstract The purpose of this paper is to give a theoretical analysis for the variational variant of the Tikhonov regularization method for solving a system of nonlinear ill-posed equations in real Hilbert spaces. Mathematics Subject Classification: 47H1

A Method for a Solution of Equilibrium Problem and Fixed Point Problem of a Nonexpansive Semigroup in Hilbert's Spaces

We introduce a viscosity approximation method for finding a common element of the set of solutions for an equilibrium problem involving a bifunction defined on a closed, convex subset and the set of fixed points for a nonexpansive semigroup on another one in Hilbert's spaces.</p