Article
Mathematics
Konrawut Khammahawong, Parin Chaipunya, Kamonrat Sombut
Summary: The aim of this research is to propose a new iterative procedure for approximating common fixed points of nonexpansive mappings in Hadamard manifolds, and discuss the convergence theorem of the proposed method under certain conditions. Numerical examples are provided to support the results for clarity. Furthermore, the suggested approach is applied to solve inclusion problems and convex feasibility problems.
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
Mathematics, Applied
Nuttapol Pakkaranang, Poom Kumam, Ching-Feng Wen, Jen-Chih Yao, Yeol Je Cho
Summary: This paper shows the existence of solutions for convex minimization problems and common fixed point problems in CAT(1) spaces under certain conditions, proposing a modified proximal point algorithm. Additionally, applications for these problems in CAT(kappa) spaces with bounded positive real number kappa are given. The results improve and generalize many recent important findings in the literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Chainarong Khunpanuk, Chanchal Garodia, Izhar Uddin, Nuttapol Pakkaranang
Summary: This article presents a new modified proximal point algorithm in the framework of CAT(1) spaces, which is used to solve common fixed point problem and minimization problems. Convergence results of the obtained process under some mild conditions are proved. Our results extend and improve several corresponding results of the existing literature.
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, Applied
Patrick L. Combettes, Lilian E. Glaudin
Summary: Various strategies are available to construct a common fixed point of nonexpansive operators iteratively by activating only a block of operators at each iteration. The proposed method achieves this goal and maintains convergence while updating only blocks of operators. Weak, strong, and linear convergence results are established by exploiting a connection with the theory of concentrating arrays.
ADVANCES IN NONLINEAR ANALYSIS
(2021)
Article
Mathematics, Applied
Hasanen A. Hammad, Hassan Almusawa
Summary: This manuscript aims to prove that the sequence {v(n)} created iteratively by a modified inertial Ishikawa algorithm converges strongly to a fixed point of a nonexpansive mapping Z in a real uniformly convex Banach space with uniformly Gateaux differentiable norm. Moreover, zeros of accretive mappings are obtained as an application. Our results generalize and improve many previous results in this direction. Ultimately, two numerical experiments are given to illustrate the behavior of the proposed algorithm.
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
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
Operations Research & Management Science
L. C. Ceng, A. Petrusel, X. Qin, J. C. Yao
Summary: Two general inertial algorithms with line-search process are proposed in this article to solve variational inequality problems with fixed-point constraints via a subgradient-extragradient approach. Common solution theorems are obtained in Hilbert spaces.
Article
Multidisciplinary Sciences
Samet Maldar
Summary: New types of parallel algorithms have been defined in this study, and their strong convergence for certain mappings with altering points has been analyzed, showing better convergence behavior compared to existing algorithms. Additionally, the concept of data dependency for these algorithms has been examined for the first time, and it has been proven that the solution of a variational inequality system can be obtained using these newly defined parallel algorithms under suitable conditions.
Article
Mathematics, Applied
Iqbal Ahmad, Mohd Sarfaraz, Syed Shakaib Irfan
Summary: The main aim of this work is to find the common solutions for a new class of extended system of fuzzy ordered variational inclusions using the XOR-operation technique. We establish the equivalence between the system of fuzzy ordered variational inclusions and a fixed point problem, and show the relationship between the system of fuzzy ordered variational inclusions and a system of fuzzy ordered resolvent equations. We prove the existence of a common solution and discuss the convergence of the iterative algorithm used to solve the problem. The results and iterative algorithm presented in this article demonstrate a significant improvement over previous known results in this field. Examples are provided to support the main results.
Article
Mathematics, Applied
Kiattiyot Juagwon, Withun Phuengrattana
Summary: In this paper, a new iterative algorithm is introduced to approximate a common element of the solution set of an equilibrium problem, the zero point set of a finite family of monotone operators, and the set of fixed points of nonexpansive mappings in Hadamard spaces. Numerical examples are also provided to solve a nonconvex optimization problem in a Hadamard space, which supports the main result.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Buthinah A. Bin Dehaish, Rawan K. Alharbi
Summary: We investigate an Ishikawa iteration process for generalized alpha-nonexpansive mappings, showing the convergence of these mappings to a common fixed point and the Delta-convergence and strong convergence of the scheme in hyperbolic space. These results amplify and refine recent ideas proposed in uniformly convex Banach spaces, including CAT(0) spaces.
Article
Mathematics, Applied
Pawicha Phairatchatniyom, Poom Kumam, Vasile Berinde
Summary: In this article, a modified Ishikawa iteration scheme is proposed to solve a fixed point problem and a split variational inclusion problem in real Hilbert spaces. Convergence theorem is proved under certain conditions. Additionally, the proposed scheme is applied to solve a split feasibility problem and compared with existing iterative schemes to demonstrate its effectiveness and performance.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Zeqing Liu, Lin Chen, Shin Min Kang, Sun Young Cho
ABSTRACT AND APPLIED ANALYSIS
(2011)
Article
Mathematics, Applied
Yan Hao, Sun Young Cho
ABSTRACT AND APPLIED ANALYSIS
(2012)
Correction
Mathematics, Applied
Xiaolong Qin, Tianze Wang, Sun Young Cho
ABSTRACT AND APPLIED ANALYSIS
(2012)
Article
Mathematics, Applied
Sun Young Cho, Xiaolong Qin, Shin Min Kang
APPLIED MATHEMATICS LETTERS
(2012)
Article
Operations Research & Management Science
Zeqing Liu, Haijiang Dong, Sun Young Cho, Shin Min Kang
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2013)
Article
Operations Research & Management Science
Xiaolong Qin, Sun Young Cho, Jong Kyu Kim
Article
Operations Research & Management Science
Xiaolong Qin, Sun Young Cho, Shin Min Kang, Feng Gu
Article
Mathematics, Applied
Shin Min Kang, Arif Rafiq, Sun Young Cho
JOURNAL OF APPLIED MATHEMATICS
(2013)
Article
Mathematics, Applied
Xiaolong Qin, Ravi P. Agarwal, Sun Young Cho, Shin Min Kang
FIXED POINT THEORY AND APPLICATIONS
(2012)
Article
Mathematics, Applied
Yuan Qing, Sun Young Cho, Meijuan Shang
FIXED POINT THEORY AND APPLICATIONS
(2013)
Article
Mathematics
Sun Young Cho, Shin Min Kang
ACTA MATHEMATICA SCIENTIA
(2012)
Article
Mathematics, Applied
Sheng Hua Wang, Sun Young Cho, Xiao Long Qin
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
(2012)
Article
Mathematics, Applied
Sun Young Cho, Shin Min Kang
FIXED POINT THEORY
(2012)
Article
Mathematics, Applied
Sun Young Cho, Xiaolong Qin, Shin Min Kang
FIXED POINT THEORY
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