Article
Mathematics, Applied
Rajat Vaish, Md Kalimuddin Ahmad
Summary: An iterative scheme for approximating the solution of a variational inequality over fixed points of an asymptotically nonexpansive mapping is introduced in this paper using the generalized viscosity implicit method and hybrid steepest-descent method. Strong convergence results for the proposed iterative scheme are established in Banach spaces. The applicability and efficiency of the proposed method in variational inclusion and convex minimization problems are demonstrated through examples, improving, extending, and unifying previously known results.
APPLIED NUMERICAL 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
Mathematics, Applied
Sabiya Khatoon, Izhar Uddin, Metin Basarir
Summary: This paper introduces a new modified proximal point algorithm based on M-iteration to approximate a common element of the set of solutions of convex minimization problems and the set of fixed points of nearly asymptotically quasi-nonexpansive mapping in CAT(0) space. The Delta-convergence of the proposed algorithm for solving common minimization problem and fixed point problem is proven. An application and numerical results based on the proposed algorithm are also provided.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Murtala Haruna Harbau, Godwin Chidi Ugwunnadi, Lateef Olakunle Jolaoso, Ahmad Abdulwahab
Summary: This work introduces a new inertial accelerated Mann algorithm for finding a point in the set of fixed points of asymptotically nonexpansive mapping in a real uniformly convex Banach space, and establishes weak and strong convergence theorems. Numerical experiments validate the algorithm's performance and show improvements over existing methods, generalizing and enhancing recent results in the literature.
Article
Mathematics
Shih-sen Chang, Lin Wang, Y. H. Zhao, G. Wang, Z. L. Ma
Summary: This paper investigates the split common fixed point problem for quasi-pseudo-contractive mappings in Hilbert spaces, proposing a new algorithm and strong convergence theorems under appropriate assumptions. The results not only enhance and extend previous findings, but also provide a positive answer to an open question.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2021)
Article
Multidisciplinary Sciences
V Pragadeeswarar, R. Gopi, M. De la Sen
Summary: The study of symmetry is crucial in nonlinear analysis, especially in proving the existence of fixed points for self mappings. This work focuses on approximating fixed points of noncyclic comparatively nonexpansive mappings in uniformly convex Banach spaces using a three-step Thakur iterative scheme, which is shown to be faster in a numerical example compared to other well-known iterative schemes. Additionally, a stronger version of the proposed theorem is provided via von Neumann sequences.
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
Multidisciplinary Sciences
Lu-Chuan Ceng, Yun-Ling Cui, Sheng-Long Cao, Bing Li, Cong-Shan Wang, Hui-Ying Hu
Summary: In this article, a pair of variational inequality and fixed-point problems (VIFPPs) are studied in a uniformly smooth and p-uniformly convex Banach space. Two parallel subgradient-like extragradient algorithms with an inertial effect are proposed to solve this pair of VIFPPs. The convergence of the algorithms is proven using suitable registrations, and an illustrative instance is provided to verify the implementability and applicability of the suggested approaches.
Article
Mathematics
Yuanheng Wang, Tiantian Xu, Jen-Chih Yao, Bingnan Jiang
Summary: This paper proposes a new method to solve the split feasibility problem and the fixed-point problem involving quasi-nonexpansive mappings. By relaxing the conditions of the operator and considering the inertial iteration and adaptive step size, our algorithm achieves better convergence and faster convergence rate compared to previous algorithms.
Article
Operations Research & Management Science
Satit Saejung, Pongsakorn Yotkaew
Summary: This paper derives Delta-convergence and strong convergence theorems for asymptotically quasi-nonexpansive sequences in Hadamard spaces, extending and improving recent results in the literature. Some of the results are even new in Hilbert spaces. Applications to convex minimization and common fixed point problems are discussed.
Article
Mathematics, Applied
Abubakar Adamu, Aisha A. Adam
Summary: In this paper, we introduce and study an inertial algorithm for approximating solutions of SEFPP in real Banach spaces. The method is applied to SEP, SEVIP, and SEEP, and is the first of its kind that does not require compactness type assumptions on the operators.
CARPATHIAN JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Truong Minh Tuyen, Nguyen Minh Trang
Summary: In this paper, two new algorithms are introduced for finding a common solution to the monotone inclusion problem, the fixed point problem for demimetric mappings, and the null point problem in a real Hilbert space, using shrinking or hybrid projection methods.
COMPUTATIONAL & APPLIED MATHEMATICS
(2022)
Article
Computer Science, Artificial Intelligence
Yekini Shehu, Qiao-Li Dong, Ziyue Hu, Jen-Chih Yao
Summary: This paper presents 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 unify several versions of fixed point methods for averaged quasi-nonexpansive mappings considered in the literature and provide several implications. Additionally, the paper demonstrates some applications of the method in solving convex and nonconvex reweighted l(Q) regularization for recovering sparse signals through numerical experiments.
Article
Mathematics, Applied
D. R. Sahu, Ajeet Kumar, Shin Min Kang
Summary: This paper introduces a modified proximal point algorithm based on the S-iteration process, to approximate a common element of the set of solutions of convex minimization problems and the set of fixed points. The algorithm is proven to have o-convergence for solving common minimization problem and common fixed point problem, generalizing and unifying existing results.
NUMERICAL ALGORITHMS
(2021)
Article
Mathematics, Applied
Nguyen Trung Hieu, Nguyen Bich Huy
Summary: This paper introduces two inertial hybrid iteration processes for finding common fixed points of mappings in Banach spaces and proves strong convergence results under suitable assumptions. The obtained results include strong convergence results in different spaces and are illustrated with numerical examples.
RICERCHE DI MATEMATICA
(2021)
