Article
Mathematics, Applied
Zheng Zhou, Bing Tan, Songxiao Li
Summary: This paper introduces an accelerated hybrid projection algorithm to solve the split common fixed point problem for demicontractive mappings. The algorithm shows strong convergence under mild conditions and numerical experiments in infinite-dimensional Hilbert spaces confirm its reliability and robustness.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
A. Taiwo, O. T. Mewomo, A. Gibali
Summary: In this paper, we studied the split common fixed point problem for demicontractive mappings in real Hilbert spaces and proposed a solution with self-adaptive step size. Numerical examples demonstrated the competitive advantage of our algorithm over existing ones. Our results extend, complement, and generalize many recent related results in the literature.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2021)
Article
Engineering, Multidisciplinary
L. B. Mohammed, A. Kilicman, A. U. Saje
Summary: In this paper, new algorithms are proposed to solve the split equality fixed-point problems for total quasi-asymptotically nonexpansive mappings in Hilbert spaces. Convergence criteria for the proposed algorithms are established and numerical results are provided to justify the theoretical results. The results of this paper provide a unified framework for studying problems involving different classes of mappings.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Mathematics
Haixia Zhang, Huanhuan Cui
Summary: This paper discusses the split common fixed point problem in Hilbert spaces and proposes a new algorithm based on inertial techniques. Two weak convergence theorems for the proposed algorithm are established under mild conditions. The stepsize in the algorithm is independent of the norm of the given linear mapping, which can enhance the algorithm's performance.
JOURNAL OF MATHEMATICS
(2021)
Article
Operations Research & Management Science
Mohammad Eslannian
Summary: In this paper, we study the split common fixed point problem for a finite family of demimetric mappings and a finite family of Bregman relatively nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We prove a strong convergence theorem of Halpern's type iteration for finding a solution of the split common fixed point problem.
Article
Operations Research & Management Science
Yaqin Wang, Xiaoli Fang, Jin-Lin Guan, Tae-Hwa Kim
Summary: This paper introduces a new viscosity iterative method for solving the split null point and common fixed point problems for maximal monotone operators and multivalued demicontractive mappings in Hilbert spaces, and obtains some strong convergence results under suitable assumptions. The results are applied to the split feasibility problem and split minimization problem, and generalize and improve upon recent findings by other authors.
Article
Mathematics, Applied
Simeon Reich, Truong Minh Tuyen
Summary: We introduce a new generalized cyclic iterative method for finding solutions of variational inequalities over the solution set of a split common fixed point problem with multiple output sets in a real Hilbert space.
NUMERICAL ALGORITHMS
(2022)
Article
Mathematics, Applied
A. Taiwo, L. O. Jolaoso, O. T. Mewomo
Summary: This paper explores the properties of firmly nonexpansive-like mappings in Banach spaces and proposes an inertial-type shrinking projection algorithm for solving split common fixed point problems, proving its strong convergence. The results complement previous research in this area and represent a novel use of inertial techniques outside of Hilbert spaces.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Operations Research & Management Science
Anteneh Getachew Gebrie
Summary: Two new self-adaptive parallel algorithms are established in this work to solve the generalized split common fixed point problem. Weak and strong convergence theorems are analyzed under suitable assumptions, generalizing and improving recent results by other authors. Several new algorithms are obtained as a direct consequence of the main algorithms, with preliminary numerical experiments provided to illustrate efficiency and implementation.
Article
Mathematics, Applied
Simeon Reich, Truong Minh Tuyen, Nguyen Thi Thu Thuy, Mai Thi Ngoc Ha
Summary: This research focuses on the split common fixed point problem with multiple output sets in Hilbert spaces. A new algorithm is proposed and a strong convergence theorem is established for solving the problem, as well as removing the assumptions on the norms of the transfer operators.
NUMERICAL ALGORITHMS
(2022)
Article
Operations Research & Management Science
Huimin He, Jigen Peng, Qinwei Fan
Summary: This paper discusses the split common fixed point problem for demicontractive operators and introduces an iterative viscosity approximation method (VAM) for solving SCFPP. It is shown that under certain conditions, the sequence generated by VAM strongly converges to a solution of SCFPP, which is identified as the unique solution of a variational inequality. The main result of this paper extends and improves upon previous results by Yao et al., Boikanyo, and Cui-Wang.
Article
Mathematics, Applied
Savita Rathee, Monika Swami
Summary: This manuscript extends the recent work of Lohawech et al. by working on the split equilibrium problem with the combined results of the fixed point problem and split variational inequality problem. The authors propose a sequence that converges weakly to the common solution of all the three problems mentioned earlier and provide some direct consequences of the main result.
Article
Mathematics, Applied
Xindong Liu, Zili Chen, Jinxing Liu
Summary: This paper proposes an algorithm to solve the split common fixed point problem for strict quasi-phi-pseudocontractive mappings in Banach spaces, proving strong convergence of the sequence generated by the algorithm. The main result is then utilized to study the split common null point problem and split quasi-inclusion problem. A numerical example is provided to illustrate the main result, which extends and improves upon previous corresponding results.
NUMERICAL ALGORITHMS
(2021)
Article
Mathematics
Huanhuan Cui
Summary: This paper focuses on multiple-sets split common fixed-point problems with demicontractive mappings. It first examines properties of demicontractive mappings and their relationship with directed mappings, and then introduces new iterative methods for solving these problems. Weak convergence of the proposed methods is established under mild conditions.
JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Jing Zhao, Yuan Li
Summary: This paper studies the split common fixed-point problem of quasi-nonexpansive operators in Hilbert space and establishes a weak convergence theorem for the proposed iterative algorithm, which combines the primal-dual method and the inertial method. The algorithm adapts step sizes self-adaptively, eliminating the need for prior information about bounded linear operator norms. Numerical results demonstrate the efficiency of the proposed algorithm.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2021)
