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The projected reflected gradient method has been shown to be a simple and elegant method for solving variational inequalities. The method involves one projection onto the feasible set and one evaluation of the cost operator per iteration and has been shown numerically to be more efficient than most available methods for solving variational inequalities. Convergence results for methods with similar elegant structures of projected reflected gradient method are still rare. In this paper, we present weak and linear convergence of a projected reflected gradient method with an inertial extrapolation step and give some applications arising from optimal control problems. We first obtain weak convergence result for the projected reflected gradient method with an inertial extrapolation step for solving variational inequalities under standard assumptions with self-adaptive step sizes. We further obtain a linear convergence rate when the cost operator is strongly monotone and Lipschitz continuous. Finally, we give some numerical applications arising from optimal control. Preliminary results show that our method is effective and efficient when compared to other related state-of-the-art methods in the literature and show the advantage gained by incorporating inertial terms into the projected reflected gradient methods. [ABSTRACT FROM AUTHOR]

We present a strongly convergent Halpern-type proximal point algorithm with double inertial effects to find a zero of a maximal monotone operator in Hilbert spaces. The strong convergence results are obtained without on-line rule of the inertial parameters and the iterates. This makes our proof arguments different from what is obtainable in the literature where on-line rule is imposed on a strongly convergent proximal point algorithm with inertial extrapolation. Numerical examples with applications to image restoration and compressed sensing show that our proposed algorithm is useful and has practical advantages over existing ones. [ABSTRACT FROM AUTHOR]

This paper presents a fully adaptive iterative method without linesearch procedure to solve variational inequalities in the setting of quasi-monotone which is locally Lipschitz. Our method involves one functional evaluation alongside one projection per iteration and our stepsizes are not restricted to be nonincreasing as opposed to relevant methods without linesearch procedure but with nonincreasing stepsizes. We give weak and strong convergence analysis of the sequences generated by our proposed method under some mild conditions. We also give R -linear rate convergence under an error bound condition and give some numerical implementations of our method. Numerical results show that our proposed method is competitive with other related methods in the literature. [ABSTRACT FROM AUTHOR]

We first establish weak convergence results regarding an inertial Krasnosel'skiĭ-Mann iterative method for approximating common fixed points of countable families of nonexpansive mappings in real Hilbert spaces with no extra assumptions on the considered countable families of nonexpansive mappings. The method of proof and the imposed conditions on the iterative parameters are different from those already available in the literature. We then present some applications to the Douglas–Rachford splitting method and image restoration problems, and compare the performance of our method with that of other popular inertial Krasnosel'skiĭ-Mann methods which can be found in the literature. [ABSTRACT FROM AUTHOR]

This paper studies modified extragradient methods with inertial extrapolation step and self-adaptive step-sizes for solving equilibrium problems in real Hilbert spaces. Strong convergence results are obtained under the assumption that the bifunction is pseudomonotone and satisfies the Lipchitz-type condition. Our method of proof is of independent interest and different from the recent arguments used in related papers on strong convergence methods with inertial steps for equilibrium problems. Numerical implementations and comparisons are given to support the theoretical findings. [ABSTRACT FROM AUTHOR]

The subgradient extragradient method with inertial extrapolation step xn + θn(xn − xn−1) (also known as inertial subgradient extragradient method) has been studied extensively in the literature for solving variational inequalities and equilibrium problems. Most of the inertial subgradient extragradient methods in the literature for both variational inequalities and equilibrium problems have not considered the special case when the inertial factor θn = 1. The convergence results have always been obtained when the inertial factor θn is assumed 0 ≤ θn < 1. This paper considers the relaxed inertial version of subgradient extragradient method for equilibrium problems with 0 ≤ θn ≤ 1. We give both weak and strong convergence results using this inertial subgradient extragradient method and also give some numerical illustrations. [ABSTRACT FROM AUTHOR]

The inertial projection and contraction method and the inertial forward-backward-forward method have been studied for solving variational inequality problems due to the ability of these methods to work well with only one projection per iteration during computations. The inertial factor in these methods is chosen to be less than 1 in most of the papers that studied these methods. It is known from a computational point of view that the efficiency of these methods improves as the inertial factor approaches 1. In this paper, we modify both the inertial projection and contraction method and the inertial forward-backward-forward method with the possibility of inertial factor taken as 1. Our proposed methods also involve a step-size rule which does not depend on the Lipschitz constant of the cost function and without any line search rule. We analyse the weak convergence of the methods under appropriate conditions. We also modify the proposed methods so that strong convergence is obtained. Preliminary computational results show that our proposed methods are promising and show better performance than some variants of inertial projection and contraction methods and inertial forward-backward-forward methods where the inertial factor is assumed to be less than 1. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative method with alternated inertial step for solving split common null point problem in real Hilbert spaces. We obtain weak convergence of the proposed iterative algorithm. Furthermore, we introduce the notion of bounded linear regularity property for the split common null point problem and obtain the linear convergence property for the new algorithm under some mild assumptions. Finally, we provide some numerical examples to demonstrate the performance and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic O (1 / n) convergence rate of our proposed algorithm in non-ergodic sense. Applications of our results to various well-known convex optimization methods, such as the proximal method of multipliers and the alternating direction method of multipliers are given. Numerical results are given to demonstrate the accelerating behaviors of our method over other related methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a single projection method with the Bregman distance technique for solving pseudomonotone variational inequalities in a real reflexive Banach space. The algorithm is designed such that its step size is determined by a self-adaptive process and there is only one computation of projection per iteration during implementation. This improves the convergence of the method and also avoids the need for choosing a suitable estimate of the Lipschitz constant of the cost function which is very difficult in practice. We prove some weak and strong convergence results under suitable conditions on the cost operator. We also provide some numerical experiments to illustrate the performance and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In the settings of real Hilbert spaces, this paper proposes modified forward– backward scheme with inertial extrapolation step for solving inverse problems. In our proposed method, it is possible for the inertial factor to be chosen as 1 unlike many previous inertial forward–backward splitting methods available in the literature. Weak and strong convergence of our proposed method are obtained under some standard conditions. In order to show the numerical advantage gained when the inertial factor is chosen as 1, a number of numerical implementations are performed on two different inverse problems: LASSO and SCAD penalty problems. [ABSTRACT FROM AUTHOR]

It is known that several optimization problems can be converted to a fixed point problem for which the underline fixed point operator is an averaged quasi-nonexpansive mapping and thus the corresponding fixed point method utilizes to solve the considered optimization problem. In this paper, we consider a fixed point method involving inertial extrapolation step with relaxation parameter to obtain a common fixed point of a countable family of averaged quasi-nonexpansive mappings in real Hilbert spaces. Our results bring a unification of several versions of fixed point methods for averaged quasi-nonexpansive mappings considered in the literature and give several implications of our results. We also give some applications to monotone inclusion problem with three-operator splitting method and composite convex and non-convex relaxed inertial proximal methods to solve both convex and nonconvex reweighted l Q regularization for recovering a sparse signal. Finally, some numerical experiments are drawn from sparse signal recovery to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods. [ABSTRACT FROM AUTHOR]

The purpose of this article is to study convergence analysis of quasi-variational inequalities using a projection-type method coupled with inertial extrapolation step. First, we give strong convergence analysis of the sequence of iterates generated by our proposed method to the unique solution of quasi-variational inequality under some mild assumptions. Later, we show that the sequence converges linearly to the unique solution in a special case of choice of parameters. Another contribution in this article is that the inertial factor in our proposed method is allowed to be equal to 1 unlike other previously proposed inertial projection-type method for solving quasi-variational inequalities in the literature where inertial factor is assumed to be bounded away from 1. [ABSTRACT FROM AUTHOR]

In this paper, we first study a relaxed inertial projection and contraction method for variational inequalities to obtain weak convergence results under standard assumptions in Hilbert spaces. Next, we propose another inertial projection and contraction method for which the inertial factor θ is chosen in [ 0 , 1 ] with θ = 1 possible. Weak and linear convergence are obtained for this second proposed method. As far as we know, the choice θ = 1 has not been considered before in the literature for inertial projection and contraction method. Finally, we give some numerical illustrations of our methods. [ABSTRACT FROM AUTHOR]

This paper studies the forward–reflected–backward splitting algorithm with momentum terms for monotone inclusion problem of the sum of a maximal monotone and Lipschitz continuous monotone operators in Hilbert spaces. The forward–reflected–backward splitting algorithm is an interesting algorithm for inclusion problems with the sum of maximal monotone and Lipschitz continuous monotone operators due to the inherent feature of one forward evaluation and one backward evaluation per iteration it possesses. The results in this paper further explore the convergence behavior of the forward–reflected–backward splitting algorithm with momentum terms. We obtain weak, linear, and strong convergence results under the same inherent feature of one forward evaluation and one backward evaluation at each iteration. Numerical results show that forward–reflected–backward splitting algorithms with momentum terms are efficient and promising over some related splitting algorithms in the literature. [ABSTRACT FROM AUTHOR]

We study two Bregman projection methods for solving variational inequality problems in real reflexive Banach spaces. Our methods have simple and elegant structures, and they require only one Bregman projection onto the feasible set and one evaluation of the cost operator at each iteration. We prove that these methods converge weakly when the cost operator is pseudomonotone on the entire space and that they converge strongly when the cost operator is strongly pseudomonotone only on the feasible set. Extensions of our proposed methods to mixed variational inequality problems are also given. Finally, we consider some examples regarding the implementation of our methods in comparisons with known methods in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the convergence analysis of an iterative algorithm with inertial extrapolation step for finding an approximate solution of split monotone inclusion problem in real Hilbert spaces. Weak convergence of the sequence of iterates generated from the proposed method is obtained under some mild assumptions. Some special cases of the general problem are given and we give some numerical implementations to support the theoretical analysis and give justification for the addition of the extrapolation step in the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, using a Bregman distance technique, we introduce a new single projection process for approximating a common element in the set of solutions of variational inequalities involving a pseudo-monotone operator and the set of common fixed points of a finite family of Bregman quasi-nonexpansive mappings in a real reflexive Banach space. The stepsize of our algorithm is determined by a self-adaptive method, and we prove a strong convergence result under certain mild conditions. We further give some applications of our result to a generalized Nash equilibrium problem and bandwidth allocation problems. We also provide some numerical experiments to illustrate the performance of our proposed algorithm using various convex functions and compare this algorithm with other algorithms in the literature. [ABSTRACT FROM AUTHOR]

We consider a scalar objective minimization problem over the solution set of another optimization problem. This problem is known as a simple bilevel optimization problem and has drawn a significant attention in the last few years. Our inner problem consists of minimizing the sum of smooth and non-smooth functions while the outer one is the minimization of a smooth convex function. We first formulate and give strong convergence analysis of an inertial algorithm for fixed-point problem of a non-expansive operator in an infinite dimensional Hilbert space. Then we convert the simple bilevel optimization problem to a fixed-point problem of a non-expansive operator in finite dimensional space and design the corresponding algorithm and establish its convergence. Our numerical experiments show that the proposed method in this paper outperforms the currently known best algorithm to solve the class of bilevel optimization problem considered. [ABSTRACT FROM AUTHOR]

We propose a new algorithm which can be considered as a combination between the subgradient extragradient method and viscosity methods for solving split common fixed points problem and variational inequality problem. We find a point which belongs to the set of common fixed points of a finite family of demimetric mappings and the common solutions to a system of variational inequalities problem for a family of monotone and Lipschitz continuous operators in a Hilbert space such that its image under a linear transformation belongs to the set of common fixed points of a finite family of demimetric mappings in uniformly convex and smooth Banach space in the image space. The strong convergence of the sequences generated by the algorithm is proved. We also give some numerical results which show that our proposed algorithms are efficient and implementable from the numerical point of view. [ABSTRACT FROM AUTHOR]

The projection methods with vanilla inertial extrapolation step for variational inequalities have been of interest to many authors recently due to the improved convergence speed contributed by the presence of inertial extrapolation step. However, it is discovered that these projection methods with inertial steps lose the Fejér monotonicity of the iterates with respect to the solution, which is being enjoyed by their corresponding non-inertial projection methods for variational inequalities. This lack of Fejér monotonicity makes projection methods with vanilla inertial extrapolation step for variational inequalities not to converge faster than their corresponding non-inertial projection methods at times. Also, it has recently been proved that the projection methods with vanilla inertial extrapolation step may provide convergence rates that are worse than the classical projected gradient methods for strongly convex functions. In this paper, we introduce projection methods with alternated inertial extrapolation step for solving variational inequalities. We show that the sequence of iterates generated by our methods converges weakly to a solution of the variational inequality under some appropriate conditions. The Fejér monotonicity of even subsequence is recovered in these methods and linear rate of convergence is obtained. The numerical implementations of our methods compared with some other inertial projection methods show that our method is more efficient and outperforms some of these inertial projection methods. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a classical pseudo-monotone and non-Lipschitz continuous variational inequality problem in real Hilbert spaces. Weak and strong convergence theorems are presented under mild conditions. Our methods generalize and extend some related results in the literature and the main advantages of proposed algorithms there is no use of Lipschitz condition of the variational inequality associated mapping. Numerical illustrations in finite and infinite dimensional spaces illustrate the behaviors of the proposed schemes. [ABSTRACT FROM AUTHOR]

We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising. [ABSTRACT FROM AUTHOR]

Our interest in this paper is to introduce a Halpern-type algorithm with both inertial terms and errors for approximating fixed point of a nonexpansive mapping. We obtain strong convergence of the sequence generated by our proposed method in real Hilbert spaces under some reasonable assumptions on the sequence of parameters. As applications, we present some strong convergence results for monotone inclusion, variational inequality problem, linear inverse problem, and LASSO problem in Compressed Sensing. Our result improves the rate of convergence of existing Halpern method for monotone inclusion, variational inequality problem, linear inverse problem and LASSO problem in compressed sensing as illustrated in our numerical examples both in finite and infinite dimensional Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an inertial projection-type method with different updating strategies for solving quasi-variational inequalities with strongly monotone and Lipschitz continuous operators in real Hilbert spaces. Under standard assumptions, we establish different strong convergence results for the proposed algorithm. Primary numerical experiments demonstrate the potential applicability of our scheme compared with some related methods in the literature. [ABSTRACT FROM AUTHOR]

In this work, we study the split common null point problem in the framework of Banach spaces. We propose an iterative scheme for solving the problem and then prove strong convergence theorem of the sequences generated by our iterative scheme under suitable conditions. We finally provide some numerical examples to support the main theorem. [ABSTRACT FROM AUTHOR]

We propose a Halpern-type forward-backward splitting with inertial extrapolation step for finding a zero of the sum of accretive operators in Banach spaces. Strong convergence of the sequence of iterates generated by the method proposed is obtained under mild assumptions. We give some numerical results in compressed sensing to validate the theoretical analysis results. Our result is one of the lew available inertial-type methods for zeros of the sum of accretive operators in Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we propose a reflected forward-backward splitting algorithm with two different inertial extrapolations to find a zero of the sum of three monotone operators consisting of the maximal monotone operator, Lipschitz continuous monotone operator, and a cocoercive operator in real Hilbert spaces. One of the interesting features of the proposed algorithm is that both the Lipschitz continuous monotone operator and the cocoercive operator are computed explicitly each with one evaluation per iteration. We then obtain weak and strong convergence results under some mild conditions. We finally give a numerical illustration to show that our proposed algorithm is effective and competitive with other related algorithms in the literature. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to introduce an extragradient-type method for solving variational inequality with uniformly continuous pseudomonotone operator. The strong convergence of the iterative sequence generated by our method is established in real Hilbert spaces. Our method uses computationally inexpensive Armijo-type linesearch procedure to compute the stepsize under reasonable assumptions. Finally, we give numerical implementations of our results for optimal control problems governed by ordinary differential equations. [ABSTRACT FROM AUTHOR]

In this paper, a projection-type approximation method is introduced for solving a variational inequality problem. The proposed method involves only one projection per iteration and the underline operator is pseudo-monotone and L-Lipschitz-continuous. The strong convergence result of the iterative sequence generated by the proposed method is established, under mild conditions, in real Hilbert spaces. Sound computational experiments comparing our newly proposed method with the existing state of the art on multiple realistic test problems are given. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of finding a common solution to a fixed point problem involving demi-contractive operator and a variational inequality with monotone and Lipschitz continuous mapping in real Hilbert spaces. Inspired by the projection and contraction method and the hybrid descent approximation method, a new and efficient iterative method for solving the problem is introduced. Strong convergence theorem of the proposed method is established under standard and mild conditions. Our scheme generalizes and extends some of the existing results in the literature, and moreover, its computational effort is less per each iteration compared with related works. [ABSTRACT FROM AUTHOR]

It is well known that the Krasnoselskii-Mann iteration of nonexpansive operators find applications in many areas of mathematics and known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a nonasymptotic convergence rate result for a Krasnoselskii-Mann iteration with inertial extrapolation step in real Hilbert spaces. We give some applications of our results to the Douglas-Rachford splitting method and the alternating projection method by John von Neumann. Our result serves as supplement to many existing results on convergence rate of Krasnoselskii-Mann iteration in the literature. [ABSTRACT FROM AUTHOR]

Using the double projection and Halpern methods, we prove two strong convergence results for finding a solution of a variational inequality problem involving uniformly continuous monotone operator which is also a fixed point of a quasi-nonexpansive mapping in a real Hilbert space. In our proposed methods, only two projections onto the feasible set in each iteration are performed, rather than one projection for each tentative step during the Armijo-type search, which represents a considerable saving especially when the projection is computationally expensive. We also give some numerical results which show that our proposed algorithms are efficient and implementable from the numerical point of view. [ABSTRACT FROM AUTHOR]

This paper presents a modification of a recently studied Malitsky–Tam forward-reflected-backward splitting method with two-step inertial extrapolation to solve nonconvex mixed variational inequalities. We give global convergence results and nonasymptotic O (1 / k) convergence rate of our proposed method under some appropriate conditions and present some mathematical justifications. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present an accelerated hybrid viscosity and steepest-descent method for solving proximal split feasibility problems (if solutions exist) in real Hilbert spaces. We obtain strong convergence of the sequence generated by our scheme under some suitable conditions on the parameters. In all our results in this work, our iterative schemes are proposed with a way of selecting the step sizes such that their implementation does not need any prior information about the bounded linear operator norm. Finally, we give numerical comparisons of our results with other established result to verify the efficiency and implementation of our new method. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to introduce a modified viscosity implicit rule for finding a common element of the set of solutions of variational inequalities for two inverse-strongly monotone operators and the set of fixed points of an asymptotically nonexpansive mapping in Hilbert spaces. Some strong convergence theorems are obtained under some suitable assumptions imposed on the parameters. As an application, we give an algorithm to solve fixed point problems for nonexpansive mappings, variational inequality problems and equilibrium problems in Hilbert spaces. Finally, we give one numerical example to illustrate our convergence analysis. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce iterative algorithm which is a combination of hybrid viscosity approximation method and the hybrid steepest-descent method for solving proximal split feasibility problems and obtain the strong convergence of the sequences generated by the iterative scheme under certain weaker conditions in Hilbert spaces. Our results improve many recent results on the topic in the literature. Several numerical experiments are presented to illustrate the effectiveness of our proposed algorithm, and these numerical results show that our result is computationally easier and faster than previously known results on proximal split feasibility problem. [ABSTRACT FROM AUTHOR]

In this paper we describe and analyse new computational technique for solving proximal split feasibility problem (SFP) using a modified proximal split feasibility algorithm. The two convex and lower semi-continuous objective functions are assumed to be non-smooth. Some application to SFP are given. We demonstrate the computational efficiency of the proposed algorithm with nontrivial numerical experiments. We also compare our method with other relevant methods in the literature in terms of convergence, stability, efficiency and implementation with our illustrative numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a generalized viscosity algorithm for finding a fixed point of an asymptotically nonexpansive mapping in the intermediate sense which is also a solution to a variational inequality problem of two inverse-strongly monotone operators in 2-uniformly smooth and uniformly convex Banach spaces. Strong convergence theorems are given under suitable assumptions imposed on the parameters. The results obtained in this paper improve and extend many recent ones in the literature. Three numerical examples are also given to show the efficiency and implementation of our results. [ABSTRACT FROM AUTHOR]

Our aim in this paper is to study strong convergence results for L-Lipschitz continuous monotone variational inequality but L is unknown using a combination of subgradient extra-gradient method and viscosity approximation method with adoption of Armijo-like step size rule in infinite dimensional real Hilbert spaces. Our results are obtained under mild conditions on the iterative parameters. We apply our result to nonlinear Hammerstein integral equations and finally provide some numerical experiments to illustrate our proposed algorithm. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study some iterative algorithms for finding a common element of the set of solutions of systems of variational inequalities for inverse-strongly accretive mappings and the set of fixed points of an asymptotically nonexpansive mapping in uniformly convex and 2-uniformly smooth Banach space or uniformly convex and q-uniformly smooth Banach space. Strong convergence theorems are obtained under suitable conditions. We also give some numerical examples to support our main results. The results obtained in this paper improve and extend the recent ones announced by many others in the literature. [ABSTRACT FROM AUTHOR]

Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common fixed point problem of demicontractive mappings in a real Hilbert space. So many authors have used algorithms involving the operator norm for solving split common fixed point problem, but as widely known the computation of these algorithms may be difficult and for this reason, authors have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. We introduce a new algorithm for solving the split common fixed point problem for demicontractive mappings with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm and then prove strong convergence of the sequence in real Hilbert spaces. Finally, we give some applications of our result and numerical example at the end of the paper. [ABSTRACT FROM AUTHOR]

The purpose of this article is to study the iterative approximation of solution to multiple sets split feasibility problems inp-uniformly convex real Banach spaces that are also uniformly smooth. We propose an iterative algorithm for solving multiple sets split feasibility problems and prove a strong convergence theorem of the sequence generated by our algorithm under some appropriate conditions inp-uniformly convex real Banach spaces that are also uniformly smooth. [ABSTRACT FROM AUTHOR]

In this paper, we propose an alternated inertial subgradient extragradient algorithm for variational inequalities with self-adaptive step-sizes and obtain weak and linear convergence results. We also obtain linear convergence results using an alternated inertial projected gradient algorithm for which knowledge of the modulus of strong pseudo-monotonicity and Lipschitz constant of the cost function are not needed. We compare numerically our algorithms with other projection-type algorithms in the literature. [ABSTRACT FROM AUTHOR]

We study the approximation of zero for sum of accretive operators using a modified Mann type forward-backward splitting algorithm and obtain strong convergence of the sequence generated by our scheme to the zero of sum of accretive operators in uniformly convex real Banach spaces which are also uniformly smooth. Our result is new and complements many recent and important results in this direction in the literature. [ABSTRACT FROM AUTHOR]

Our purpose in this paper is to prove strong convergence theorems using the modified Mann type iteration for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping in the framework of reflexive real Banach spaces. We also discuss the approximation of a fixed point of a left Bregman strongly nonexpansive mapping which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature. [ABSTRACT FROM AUTHOR]

Our purpose in this paper is to prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature. [ABSTRACT FROM AUTHOR]

Our purpose in this paper is to obtain strong convergence result for approximation of solution to constrained convex minimization problem using a new iterative scheme in a real Hilbert space. Furthermore, we give numerical analysis of our iterative scheme. [ABSTRACT FROM AUTHOR]