Article
Engineering, Multidisciplinary
Javad Balooee, Shih-Sen Chang, Jen-Chih Yao
Summary: The main contribution of this work is the construction of a new iterative algorithm for solving a new class of set-valued variational-like inclusion problems in the setting of Banach spaces. The convergence analysis of the proposed algorithm is studied under some appropriate conditions. The final section focuses on the investigation and analysis of the notion of (H(., .), eta)-accretive operator introduced and studied by Wang and Ding (2010).
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
(2023)
Article
Mathematics, Applied
Li-Jun Zhu, Zhangsong Yao
Summary: In this paper, a splitting method is proposed to solve a variational inclusion problem and a pseudomonotone variational inequality problem in a real Hilbert space. This method combines a forward-backward type method and a modified extragradient method with self-adaptive techniques. It is proven that the sequence generated by the splitting method strongly converges to a common solution of the variational inclusion and the pseudomonotone variational inequality.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2023)
Article
Mathematics, Applied
Javad Balooee, Shih-sen Chang, Min Liu, Jen-Chih Yao
Summary: In this article, we construct a new iterative scheme based on the resolvent operator method to find a common element of the solution set of a generalized variational inclusion problem and the set of fixed points of a total asymptotically nonexpansive mapping in a real Banach space. We prove the strong convergence of the sequence generated by our proposed algorithm to a common element of these two sets under certain parameter controlling conditions. Our second goal is to investigate and analyze the concept of H(.,.)-accretive operator mentioned in the literature and provide some comments and new examples.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
(2023)
Article
Mathematics, Applied
Youli Yu, Yeong-Cheng Liou
Summary: This paper investigates the split variational inclusion problem in Hilbert spaces and proposes an iterative algorithm with an inertial item for finding a solution. The strong convergence of the suggested algorithm is proved under certain conditions.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2021)
Article
Operations Research & Management Science
T. Kowan, S. Suwansoontorn, T. Jitpeera, C. Mongkolkeha
Summary: In this paper, the viscosity explicit method is developed to find a solution of the variational inclusion problem in Banach spaces. The method combines the algorithms defined by Cholamjiak, Pholasa, Suantai, and Sunthrayuth [doi: 10.1080/02331934.2020.1789131] and by Wang, Wang, and Zhang [doi: 10.1080/02331934.2019.1705299]. A new suitable assumption is also provided to prove the strong convergence theorem. The proposed method is applied to various problems and numerical examples are given to compare its performance with other methods.
Article
Engineering, Multidisciplinary
Javad Balooee, Shih-Sen Chang, Jen-Chih Yao
Summary: The main contribution of this paper is the development of a new iterative algorithm for solving a new class of set-valued variational-like inclusion problems in Banach spaces. The convergence analysis of the iterative sequences generated by the algorithm is studied, and the notion of (H(., .), eta)-accretive operator is investigated and analyzed as well. The paper concludes with important comments on (H(., .), eta)-accretive operator and related results in the literature.
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
(2023)
Article
Mathematics, Applied
Emeka C. Godwin, Chinedu Izuchukwu, Oluwatosin T. Mewomo
Summary: In this article, a new efficient self-adaptive method is proposed and proven to strongly converge to a minimum-norm solution of a generalized split feasibility problem. The method combines relaxation and inertial techniques, and employs simple self-adaptive stepsizes. It provides a solution to other classes of generalized split feasibility problems.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Operations Research & Management Science
Bijaya K. Sahu, George Nguyen, Gayatri Pany, Ouayl Chadli
Summary: In this paper, we define the generalized densely relaxed eta-alpha pseudomonotonicity and relaxed eta-alpha quasimonotonicity, and establish the existence of solutions for generalized variational-like inequalities with these monotonicity notions. The results improve and generalize existing literature, and provide an alternative to certain wrong results in the literature related to the studied problem.
Article
Mathematics, Applied
Jenwit Puangpee, Suthep Suantai
Summary: This paper introduces and analyzes a new parallel algorithm for finding a common solution of a system of quasi-variational inclusion problems and a common fixed point of a finite family of nonexpansive mappings in a q-uniformly Banach space. A strong convergence theorem of the proposed algorithm is established under some control conditions. The main results are applied to solve convex minimization problems, multiple sets variational inequality problems, and multiple sets equilibrium problems, with numerical experiments of image restoration problems provided as support.
FIXED POINT THEORY
(2021)
Article
Mathematics, Applied
Javad Balooee, Jen-Chih Yao
Summary: In this paper, the solutions of a new system of generalized multi-valued variational-like inclusions involving -H-77-accretive mappings are found using resolvent operator technique and Nadler's technique. The Lipschitz continuity of the resolvent operator associated with a H-?-accretive mapping is proven and its Lipschitz constant is computed. A new equivalence relationship between a sequence of fi-n-accretive mappings and their associated resolvent operators is established. An iterative algorithm is constructed to find an approximate solution of the system, and the convergence analysis is studied.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2023)
Article
Mathematics
Rais Ahmad, Mohd Ishtyak, Arvind Kumar Rajpoot, Yuanheng Wang
Summary: This paper investigates a system of mixed variational inclusions involving a generalized Cayley operator and the generalized Yosida approximation operator. An iterative algorithm is proposed to discuss the convergence analysis. It is shown that the system has a unique solution by utilizing the properties of q-uniformly smooth Banach space, and the convergence criteria for sequences generated by the iterative algorithm are discussed.
Article
Mathematics, Applied
Yury Arlinskii, Christiane Tretter
Summary: This paper establishes necessary and sufficient conditions for the domain equality dom A = dom A* and for the equality Re A = AR of operator real part Re A and form real part AR for unbounded maximal sectorial operators. The natural question of whether dom A = dom A* implies Re A = AR for a maximal sectorial operator A is answered negatively in this paper. Families of unbounded coercive m-sectorial operators A are constructed to illustrate this.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Operations Research & Management Science
Javad Balooee, Suliman Al-Homidan
Summary: This paper investigates a generalized nonlinear implicit variational-like inclusion problem involving an (A, eta)-maximal m-relaxed monotone mapping and the set of fixed points of a total asymptotically nonexpansive mapping. A new iterative algorithm is constructed and the strong convergence of the sequence generated by the algorithm is proven to a point belonging to the intersection of the two sets.
Article
Engineering, Multidisciplinary
Preeyanuch Chuasuk, Ferdinard Ogbuisi, Yekini Shehu, Prasit Cholamjiak
Summary: This paper introduces a new inertial iterative method for solving split variational inclusion problems in real Hilbert spaces. The method increases the rate of convergence by inertial extrapolation step, relaxes the choice of inertial factor, and shows numerical efficiency and superiority through test examples.
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
(2021)
Article
Mathematics, Applied
Javad Balooee, Shih-sen Chang, Min Liu, Jinhua Zhu
Summary: The main objective of this paper is to construct a new iterative algorithm using the notion of P-eta-resolvent operator for solving a new system of generalized multi-valued variational-like inclusions in the setting of Banach spaces. As an application of the constructed algorithm, the strong convergence of the sequences generated by our proposed iterative algorithm to a solution of the system of generalized multi-valued variational-like inclusions is proved.
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
(2022)
