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In this paper, for finding a common zero of a finite family of m-accretive mappings in uniformly convex Banach spaces with a uniformly Gâteaux differentiable norm, we propose an implicit iteration algorithm and an explicit one, based on a convex combination of the steepest-descent method and a composition of resolvents. We also show that our main algorithm contains some iterative ones in literature as special cases. Finally, we give numerical examples for illustration.

In this paper, we introduce iterative regularization methods for solving the multiple-sets split feasibility problem, that is to find a point closest to a family of closed convex subsets in one space such that its image under a bounded linear mapping will be closest to another family of closed convex subsets in the image space. We consider the cases, when the families are either finite or infinite. We also give two numerical examples for illustrating our main method.

In this paper, for solving the variational inequality problem over the set of common fixed points of a finite family of demiclosed quasi-nonexpansive mappings in Hilbert spaces, we propose two new strongly convergent methods, constructed by specific combinations between the steepest-descent method and the block-iterative ones. The strong convergence is proved without the boundedly regular assumptions on the family of fixed point sets as well as the approximately shrinking property for each mapping of the family, that are usually assumed in recent literature for similar problems. Applications to the multiple-operator split common fixed point problem (MOSCFPP) and the problem of common minimum points of a finite family of lower semi-continuous convex functions with numerical experiments are given.

In this paper, we present a new approach to the problem of finding a common zero for a system of m†accretive mappings in a uniformly convex Banach space with a uniformly GA¢teaux differentiable norm. We propose an implicit iteration method and two explicit ones, based on compositions of resolvents with the steepest†descent method. We show that our results contain some iterative methods in literature as special cases. An extension of the Xu's regularization method for the proximal point algorithm from Hilbert spaces onto Banach ones under simple conditions of convergence and a new variant for the method of alternating resolvents are obtained. Numerical experiments are given to affirm efficiency of the methods.

In this paper, we introduce implicit and explicit iterative methods for solving a variational inequality problem over the set of zeros for a maximal monotone mapping in Hilbert spaces. As consequence, new modifications of the proximal point method are obtained.

In this paper, for the multiple-sets split feasibility problem, that is to find a point closest to a family of closed convex subsets in one space such that its image under a linear bounded mapping will be closest to another family of closed convex subsets in the image space, we study several iterative methods for finding a solution, which solves a certain variational inequality. We show that particular cases of our algorithms are some improvements for existing ones in literature. We also give two numerical examples for illustrating our algorithms.

In this paper, in order to solve the multiple-sets split feasibility problem in Hilbert spaces, we introduce the regularization methods of Lavrentiev’s and Bruck–Bakushinskii’s type, where the iterative parameter is chosen independently of the operator norm. We also consider some particular cases of the introduced methods. Applications and numerical experiments are given for illustration and comparison.

In this paper, in order to solve a variational inequality problem over the fixed point set of a nonexpansive mapping on uniformly smooth or reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm, we investigate an explicit iteration method, based on the steepest-descent and Krasnosel’skii–Mann algorithms. We also show that some modifications of the last and Halpern-type algorithms are special cases of our result.

In this paper we study the Browder–Tikhonov regularization method for finding a common solution for a system of nonlinear ill-posed equations with potential, hemicontinuous and monotone mappings in Banach spaces. We give a principle, named quasi-residual, to choose a value of the regularization parameter and an estimate of convergence rates for the regularized solutions.

In this paper, we introduce implicit and explicit iterative methods for finding a zero of a monotone variational inclusion in Hilbert spaces. As consequence, an improvement modification of an algorithm existing in literature is obtained. A numerical example is given for illustrating our algorithm.

In this paper, we propose a new simple explicit iterative algorithm to find a solution for variational inequalities over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm. Two numerical examples also are given for illustration.

In this paper, in order to solve a variational inequality problem over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformlyGâteaux differentiable norm, we introduce two new explicit iteration methods.

In this paper, in order to solve nonlinear ill-posed operator equations involving an m-accretive mapping on a real Banach space, that does not admit a weak sequential continuous duality mapping, we prove a strongly convergent theorem for Newton-Kantorovich iterative regularization method with a posteriori stopping rule. In our results, the Lipschitz continuity of the derivatives for the mapping is not necessary.

In this paper, in order to solve mathematical programs with generalized nonlinear comple-mentarity constraints, we present a new regularization method of Tikhonov type, based on regularizing an optimization problem with equality constraints. The stability and convergence of the regularized solutions are considered. Numerical examples are given for illustration.

In this paper, we propose a new simple parallel iterative method to find a solution for variational inequalities over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm. Our parallel iterative method is simpler than the one proposed by Buong et al. (Numer. Algorithms 72, 467–481 2016). An iterative method of Halpern type for common zeros of an infinite family of m-accretive mappings is shown as a special case of our result. Two numerical examples are also given to illustrate the effectiveness and superiority of the proposed algorithm.

In this paper, in order to solve a variational inequality problem over the set of common fixed points of an infinite family of nonexpansive mappings on a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm, we introduce two new implicit iteration methods. Their strong convergence is proved, by using new V-mappings instead of W-ones.

In this paper we prove strong convergence of the Browder-Tikhonov regularization method and the regularization inertial proximal point algorithm to a solution of nonlinear ill-posed equations involving m-accretive mappings in real, reflexive, and strictly convex Banach spaces with a uniformly Gâteaux differentiable norm without weak sequential continuous duality mapping.

In this paper, we introduce two regularization methods, based on the Browder-Tikhonov and iterative regularizations, for finding a solution of variational inequalities over the set of common fixed points of an infinite family of nonexpansive mappings on real reflexive and strictly convex Banach spaces with a uniformly Gateaux differentiate norm.

In this paper, we introduce a new explicit iterative algorithm for finding a solution for variational inequalities over the set of common fixed points of a finite family of nonexpansive maps on Hilbert spaces. An application and a numerical result are given for illustration.

In this paper, we introduce a new iteration method based on the hybrid method in mathematical programming and the descent-like method for finding a common element of the set of solutions for a variational inequality and the set of fixed points for a nonexpansive mapping in Hilbert spaces. Our method modifies and improves some methods in literature.

The purpose of this paper is to prove the strong convergence of a method combining the descent method and the hybrid method in mathematical programming for finding a point in the common fixed point set of a semigroup of nonexpansive mappings in Hilbert space.

The aim of the paper is to propose an iterative regularization method of proximal point type for finding a common solution for a finite family of inverse-strongly monotone equations in Hilbert spaces.

The purpose of this paper is to investigate the Tikhonov regularization method for solving a system of ill-posed equilibrium problems in Banach spaces with a posteriori regularization-parameter choice. An application to convex minimization problems with coupled constraints is also given.

The purpose of this paper is to present a regularization variant of the extragradient method for finding a common element of the solution sets for a variational inequality problem involving a \( \tilde k \)-Lipschitz continuous monotone mapping A and for a finite family of λi-inverse strongly-monotone operators {Ai}i = 1Nfrom a closed convex subset K into the Hilbert space H.

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.

The goal of this study is to analyze the Tikhonov regularization method as applied to a general nonlinear optimization problem that has been previously reduced to an unconstrained optimization problem. The stability properties of the method are examined, and its convergence is proved.

The purpose of this paper is to present an itertaive regularization method of zero order for finding a common element of the solution set for a variational inequality problem involving a Lipschitz continuous monotone mapping A0 and for a finite family of λi strictly pseudocontractive mappings {Ti} N=1 from a closed convex subset C into Hilbert

In this paper, two parallel methods for solving systems of accretive operator equations in Banach spaces are studied. The convergence analysis of the methods in both free-noise and noisy data cases is provided., Comment: 24 pages

An operator regularization method is considered for ill-posed vector optimization of weakly lower semicontinuous essentially convex functionals on reflexive Banach spaces. The regularization parameter is chosen by a modified generalized discrepancy principle. A condition for the estimation of the convergence rate of regularized solutions is derived.

A class of a posteriori parameter choice strategies for the operator version of Tikhonov regularization (including variants of Morozov's and Arcangeli's methods) is proposed and used in investigating the rate of convergence of the regularized solution for ill–posed nonlinear equation involving a monotone operator in Banach space.

In this paper, we study an operator version of the modified Browder-Tikhonov regularization method for finding a common solution for a system of ill-posed operator equations involving m-accretive operators Ai, i =0 , ... , N, in a reflexive Banach space. The convergence rates of the regularized solutions are estimated not only in the infinite-dimensional space, but also in connection with its finite-dimensional approximations without the weakly sequential continuity of the dual mapping. MSC: 47H17; 47H20

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 ofλi-inverse-strongly monotone mappings in Hilbert spaces.

Convergence rates are justified for regularized solutions of a Hammerstein operator equation of the form x + F 2 F 1(x) = f in the Banach space with monotone perturbations f 2 and f 1 .

The aim of this paper is to present an existence theorem of optimal control for systems descrided by the operator equation of Hammerstein type $x + K F(u, x) = 0$ with the discontinuous monotone nonlinear operator $F$ in $x$. Then, the theoretical result is applied to investigate an optimal control problem for system, where the state is written in the form of nonlinear integral equations in $L_p(\omega)$.

The purpose of this note is to study a convergence for a method in form of combination of discrete approximations with regularization for solving operator equations of Hammerstein's type in Banach spaces. For illustration, an example in the theory of nonlinear integral equations is given.

In this note we study a variational method of regularization to solve nonlinear ill-posed problems involving monotone operators in infinite dimensional Banach space, when perturbative operators are non - monotone, basing on minimization of norm in interpolation space over closed and convex sets.

In this paper, we present a regularized parameter choice in a new regularization method of Browder-Tikhonov type, for finding a common solution of a finite system of ill-posed operator equations involving Lipschitz continuous and accretive mappings in a real reflexive and strictly convex Banach space with a uniformly Gateaux differentiate norm. An estimate for convergence rates of regularized solution is also established.