Article
Multidisciplinary Sciences
Linqi Sun, Hongwen Xu, Yan Ma
Summary: In this paper, a new implicit iterative algorithm is proposed for finding the common fixed point set of nonexpansive mappings in a reflexive Hilbert space, using the viscosity approximation method and the hybrid steepest-descent iterative method. The algorithm is shown to strongly converge to the unique solution of a class of variational inequalities under certain conditions. It is also generalized to a broader family of mappings and equilibrium problems, and the stability and effectiveness of the algorithm are verified through numerical results and comparisons with existing algorithms.
Article
Mathematics, Applied
Hui Huang, Xue Qian
Summary: This paper studies the existence of a common fixed point for a pair of mappings without assuming a fixed and less than 1 contractive coefficient. By replacing the fixed contractive coefficient with a nonlinear contractive function, we establish a unique common fixed point theorem for a pair of asymptotically regular self-mappings in a metric space. Moreover, we prove that a pair of nonexpansive and continuous self-mappings defined on a nonempty closed convex subset of a Banach space have a common fixed point by the asymptotical regularity of two approximate mappings. The examples given illustrate that our results extend a recent result in the literature.
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
L. C. Ceng, C. S. Fong
Summary: This paper introduces a general viscosity-type extragradient method for solving the fixed point problem of an asymptotically nonexpansive mapping and the variational inclusion problem with two accretive operators. A strong convergence theorem is obtained in the setting of Banach spaces, and the application of this method in solving fixed point and variational inequality problems in Hilbert spaces is established. The strong convergence result is then applied to illustrate an example involving the variational inequality and fixed point problems.
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
Shih-sen Chang, Jinfang Tang, Chingfeng Wen
Summary: The article introduces a new algorithm that proves the convergence of a sequence to a common element in the set of fixed points for quasi-pseudo-contractive mappings and demi-contraction mappings, as well as the set of zeros of monotone inclusion problems on Hadamard manifolds. The results are then applied to study minimization problems and equilibrium problems in Hadamard manifolds.
ACTA MATHEMATICA SCIENTIA
(2021)
Article
Mathematics, Applied
Muhammad Waseem Asghar, Mujahid Abbas
Summary: In this paper, a new self-adaptive viscosity type algorithm is introduced for solving split common fixed point, variational inequality, split common null point, optimization, and hierarchical variational inequality problems. It is proven that the sequence generated by this algorithm strongly converges to a solution of the split common fixed point problem under appropriate conditions, which is identified as the unique solution of a variational inequality problem. A numerical example is provided to illustrate the effectiveness of the proposed approach. The results presented in this paper improve and generalize existing results in the literature.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2023)
Article
Mathematics
Atid Kangtunyakarn, Sarawut Suwannaut
Summary: In this research, we introduced the concept of S-mapping generated by a finite family of contractive mappings, Lipschitzian mappings, and finite real numbers. We then proved the strong convergence theorem for the fixed point sets of the finite family of contraction and Lipschitzian mappings, as well as the solution sets of the modified generalized equilibrium problem. Numerical examples were provided to illustrate the main theorem.
JOURNAL OF MATHEMATICS
(2022)
Article
Multidisciplinary Sciences
Rahul Shukla, Rajendra Pant, Winter Sinkala
Summary: This article introduces the importance of fixed point theory in studying symmetry in mathematics, and presents a new iterative method to approximate fixed points of nonexpansive mappings. The stability of this method is studied and convergence theorems are established under certain geometrical assumptions. Several applications in the field of nonlinear analysis are also presented.
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
Mathematics, Applied
Shahram Rezapour, Ching-Feng Wen, Seyyed Hasan Zakeri
Summary: In this paper, a new iterative method is introduced for solving split feasibility, variational inclusion, and fixed point problems involving nonexpansive and k-strictly pseudo-contractive mappings. It has been proved that under suitable conditions, the algorithms strongly converge to the minimum-norm solution of these problems.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2021)
Article
Mathematics, Applied
Mohd Asad
Summary: In this article, a new inertial algorithm is proposed and studied, which combines inertial extrapolation, S-iteration process, and viscosity approximation method to compute a common solution of an equilibrium problem and a family of nonexpansive operators in real Hilbert space. The suggested algorithm is shown to have strong convergence under simple assumptions on control sequences. Furthermore, a comparative analysis with existing well-known algorithms is conducted using an analytical example. The results of this paper have improved, generalized, and extended some prominent recent findings in this field.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Operations Research & Management Science
Shih-sen Chang, J. C. Yao, Ching-Feng Wen, Li Juan Qin
Summary: This paper aims to find a common element in the intersection of the set of zeros of the inclusion problem of sum of two monotone mappings and the set of fixed points of a Bregman quasi nonexpansive mapping in a reflexive Banach space using Bregman distance and shrinking projection method. Some strong convergence theorems are proved under suitable conditions, and the results are applied to study the convex minimization problem and the variational inequality problem.
Article
Mathematics, Applied
Nosheen Zikria, Aiman Mukheimer, Maria Samreen, Tayyab Kamran, Hassen Aydi, Kamal Abodayeh
Summary: In this paper, we introduce gs;omega-families of generalized pseudo-b-distances in b-gauge spaces (U, Qs;omega) and define gs;omega-sequential completeness and construct an F-type contraction T : U - U using these families on U. Furthermore, we develop novel periodic and fixed point results for these mappings in the setting of b-gauge spaces using gs;omega-families on U, which generalize and improve some of the results in the corresponding literature. The validity and importance of our theorems are demonstrated through an application involving the existence solution of an integral equation.
Article
Mathematics, Applied
Mohammad Dilshad, Aysha Khan, Mohammad Akram
Summary: This article introduces and analyzes the splitting type viscosity methods for solving inclusion and fixed point problems of a nonexpansive mapping on Hadamard manifolds. The convergence of sequences generated by the proposed iterative methods is derived under certain assumptions, with discussions on special cases and applications.