We address the split feasibility problem with convex sublevel sets that are computationally expensive to project onto. Instead of conventional half-space approximations, we introduce a moving ball projection method based on a sequence of closed balls inside the sublevel sets. These projections are computationally efficient and admit closed-form solutions. Moreover, the method preserves feasibility at every iterate, promoting faster convergence. We establish global convergence under mild assumptions and demonstrate the algorithm's effectiveness through numerical examples. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

This paper addresses the split feasibility problem with multiple output sets in Hilbert spaces, wherein the feasibility sets are represented as sublevel sets of convex functions. In contrast to existing relaxed projection algorithms wherein half-spaces are constructed in distinct Hilbert spaces, the proposed approach constructs all half-spaces uniformly within a single Hilbert space. Based upon this conceptual framework, several relaxed projection algorithms are developed. Under standard conditions, the convergence of these algorithms is rigorously established. Numerical experiments demonstrate the effectiveness of the proposed algorithms and provide comparisons with existing relaxed projection methods.

We introduce a class of selective max-residual operators for approximating common fixed points of finite families of cutters in real Hilbert spaces. By adaptively selecting at each iteration the component with the maximal residual, these operators preserve the fundamental properties of the underlying cutters. We establish weak and strong convergence theorems under standard assumptions. The theoretical framework is applied to develop computationally efficient algorithms for the split feasibility problem with multiple output sets and the multiple-sets split feasibility problem, eliminating the need for prior knowledge of the norms of the linear operators involved.

This paper addresses the multiple-operator split common fixed point problem, a fundamental challenge with wide applications in signal processing and medical imaging. We propose new block iterative algorithms, extending existing approaches to handle more demicontractive operators. Our key contributions are: firstly, introducing adaptive step-size mechanisms that remove the need to estimate the norm of linear operators; secondly, developing extrapolated Landweber operators to enhance convergence; and thirdly, formulating a double cyclic projection method to enhance flexibility and efficiency. We establish the weak convergence of these methods under intermittent activation of operator blocks through theoretical analysis. Numerical experiments demonstrate the algorithms’ effectiveness and efficiency in solving tough problems.

This study aims to address the problem of finding a common fixed point for multiple finite demicontractive mappings. We begin by examining the fundamental characteristics of the convex combination of these mappings. Then, we propose a new approach to establish the strong convergence of Thong and Hieu's method, even under weak convergence criteria. Notably, we have made two significant improvements compared to previous research. Our numerical experiments confirm the effectiveness of our proposed convergence criteria, resulting in substantial enhancements in the method's performance.

In this paper, we focus on the split common fixed point problem for hemicontractive mappings. We introduce two novel iterative methods for this problem and demonstrate their weak convergence under certain mild conditions. Our methods, in comparison to existing methods, offer a larger range of stepsize parameters, thereby enhancing the method's efficiency.

In this paper, we investigate split common fixed-point problems with multiple output subsets when the involved nonlinear mappings are demicontractive. By exploring the properties of demicontractive mappings, we further weaken the condition on the step size, which ensures the convergence of iterative methods for solving such problems. The preliminary experimental findings provide compelling empirical evidence substantiating the effectiveness of the proposed step size.

In this paper, we present a modified projection and contraction method for solving quasi-monotone variational inequalities in real Hilbert spaces. Our proposed method is a combination of double inertial extrapolation steps, the subgradient extragradient method and the projection contraction method, which can effectively accelerate the convergence rate. The weak and linear convergence have been obtained under some suitable conditions. Some numerical experiments are given to show that our proposed method outperforms the related methods.

In this paper, we introduce a new relaxed method for solving the split feasibility problem in Hilbert spaces. In our method, the projection to the halfspace is replaced by the one to the intersection of two halfspaces. We give convergence of the sequence generated by our method under some suitable assumptions. Finally, we give a numerical example for illustrating the efficiency and implementation of our algorithms in comparison with existing algorithms in the literature.

In this paper, we present two novel multi-step inertial iterative methods to approximate a common element that combines equilibrium problems with other problems in real Hilbert spaces. Firstly, by combining equilibrium problems, fixed point problems and a general system of variational inequalities, we adopt a conjugate gradient method to solve them. Secondly, by integrating equilibrium problems, fixed point problems and split feasibility problems, we employ a S -iteration process to address them. Under appropriate assumptions and mild conditions, we obtain strong convergence theorems of our proposed algorithms. Finally, some numerical experiments are provided to test and verify the efficiency of the proposed algorithms.

In this paper, we introduce two new iterative algorithms, Halpern-Krasnosel'skiI-Mann iteration (HKM) and the Krasnosel'skiI-Mann-Halpern iteration (KMH) for fixed points of nonexpansive mappings. Under mild conditions, we proved the strong convergence theorems of the algorithms for fixed points of nonexpansive mappings in Hilbert spaces. Finally, we give a numerical example for illustrating the efficiency of the given algorithms in comparison with existing algorithms in the literatures.

In this paper, we investigate a split common fixed point problem with multiple output sets within a more general framework and we present a novel iterative method that boasts the advantage of the step size calculation that is independent of the norm of linear mappings. We prove the weak convergence of the method and the strong convergence of its variants under certain conditions. Furthermore, we apply our main results to the split feasibility problem with multiple output sets. Our numerical results indicate that our method is an effective approach to this problem.

In this paper, we investigate the generalized Halpern iteration for computing fixed points of nonexpansive mappings in Hilbert space setting, and prove the strong convergence under new control conditions on parameters. The convergence results generalize the existing ones in the literature. We also present a convergence rate analysis for the generalized Halpern iteration with a particular choice of parameters. Finally, we give an application to the split feasibility problem and two numerical examples for illustrating the performance of the algorithm.

In this article, we propose four alternated inertial algorithms for finding a common solution of equilibrium problems and split feasibility problems in Hilbert spaces. We present a variable step size, which is not required to know the operator norm. Furthermore, these algorithms adopt the new convex subset form by a sequence of closed balls instead of half spaces, and it is easy to calculate the projections onto these sets. We establish strong and weak convergence theorems of these algorithms under some proper assumptions and also present a numerical experiment to illustrate the performance and the advantage of the proposed algorithms.

为了研究振动压路机钢轮在振动压实作业不同阶段的动力学响应,引入状态向量σ来描述钢轮与路基之间的相互作用,引入塑性参数ε来描述路基的弹塑性状态,建立了振动压路机-路基耦合动力学模型.基于该模型,采用数值积分的方法,得到了钢轮响应的时间历程、相图、频谱、庞加莱截面、分岔图等,对不同塑性参数路基上钢轮的动态响应进行了分析.结果表明:随着压实作业的进行,振动压路机钢轮会经历"单周期运动-倍周期运动-混沌运动"的动力学演化,在单周期运动时存在与路基持续和周期性失去接触的工况,在倍周期以及混沌运动时出现"跳振"现象.

In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.

In Hilbert spaces, we study the split feasibility problem with multiple output sets for demicontractive mappings. For solving this problem, we propose an iterative method and construct two selection strategies of stepsizes, namely the fixed stepsize and the variable stepsize. Under appropriate conditions, we prove the weak convergence of the proposed iterative method and the strong convergence of its variant. Furthermore, the experimental results show that the stepsize we constructed is very helpful to improve the convergence speed of the iterative method.

In recent years, the Douglas-Rachford algorithm has received much attention due to its various applications in image recovery, signal processing, and machine learning. In this paper, we introduce the Mann iteration of Douglas-Rachford algorithm with a new error sequence in Hilbert spaces, and establish its weak convergence under some mild conditions. Furthermore, we propose the Halpern iteration of Douglas-Rachford algorithm with two different error sequences, and prove their strong convergence under some proper conditions. Finally, a feasibility problem is also considered.

Inertial algorithms for solving variational inequality problems with Lipschitz continuous and monotone mappings, equilibrium problems and fixed point problems involved in nonexpansive mappings and k-strictly pseudocontractive mappings in Hilbert spaces are proposed. We provide a strong convergence theorem and a weak convergence theorem for the proposed algorithms under mild conditions and give some applications on the inertial algorithms.

ABSTRACT In recent years, the Forward-Backward algorithm (FBA) received much attention due to its various applications in image recovery, signal processing, and machine learning. In this paper, we consider the FBA in the setting of Banach spaces that are uniformly convex and q-uniformly smooth. We introduce two viscosity FBA, and one of them with weakly contractive mapping, which generalizes many previous results on the viscosity approximation method with fixed contraction. Moreover, we establish their strong convergences under more general conditions.