Article
Mathematics
Lu-Chuan Ceng, Yekini Shehu, Jen-Chih Yao
Summary: In this paper, we investigate two modified Mann subgradient-like methods to find a solution to pseudo-monotone variational inequalities in a real Hilbert space, which is also a common fixed point of a finite family of nonexpansive mappings and an asymptotically nonexpansive mapping. We obtain strong convergence results for the sequences constructed by these proposed rules and provide examples to illustrate our analysis.
Article
Mathematics, Applied
Lu-Chuan Ceng, Jen-Chih Yao
Summary: This article presents two Mann-type inertial subgradient extragradient iterations for finding a common solution of the VIP and CFPP problems. The iterative schemes are efficient and require minimal calculations, with strong convergence theorems established without assuming sequentially weak continuity for the mappings involved. The applicability and implementability of the algorithms are demonstrated through two illustrative examples.
Article
Operations Research & Management Science
Lu-Chuan Ceng, Meijuan Shang
Summary: This paper introduces hybrid inertial subgradient extragradient algorithms to solve variational inequality problems and common fixed-point problems, and proves the strong convergence of the algorithms under mild conditions.
Article
Mathematics, Applied
Lateef Olakunle Jolaoso, Adeolu Taiwo, Timilehin Opeyemi Alakoya, Oluwatosin Temitope Mewomo, Qiao-Li Dong
Summary: This paper introduces a method for finding a common solution of a Variational Inequality Problem and the fixed point of quasi-nonexpansive mapping, with a strong convergence proof. The method does not require computation of projection onto the feasible set of the VIP, making it simple and easy to implement computationally.
COMPUTATIONAL METHODS IN 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
Gang Cai, Qiao Li Dong, Yu Peng
Summary: In this paper, a new algorithm is proposed for solving variational inequality problems and fixed point problems in real Hilbert spaces. Strong convergence theorems are derived under appropriate conditions. Numerical experiments are conducted to demonstrate the advantages of the proposed algorithm.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2022)
Article
Mathematics, Applied
Jaroslaw Gornicki, Ravindra K. Bisht
Summary: This paper discusses how studying the existence of fixed points of averaged mappings T-lambda = (1 - lambda)I +lambda T, where 0 < lambda < 1 and I is the identity operator, can help in the study of existence of fixed points of mappings T for a general mathematical audience.
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Jeremiah N. N. Ezeora, Cyril D. D. Enyi, Francis O. O. Nwawuru, Richard C. C. Ogbonna
Summary: In this article, we study split equilibrium fixed-point problems involving pseudomonotone bifunctions that satisfy Lipschitz-type continuous condition and nonexpansive mappings in real Hilbert spaces. To solve this problem, we propose an inertial extragradient algorithm and establish a strong convergence theorem using the algorithm sequence under mild conditions. A numerical example demonstrates the efficiency of our algorithm and its superiority over the algorithm studied by Narin in 2019.
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Emeka C. Godwin, Timilehin O. Alakoya, Oluwatosin T. Mewomo, Jen-Chih Yao
Summary: This paper introduces a new relaxed inertial Tseng extragradient method with self-adaptive step size for approximating common solutions of monotone variational inequality and fixed point problems of quasi-pseudo-contraction mappings in real Hilbert spaces. The paper proves a strong convergence result for the proposed algorithm without the knowledge of the Lipschitz constant of the cost operator. Furthermore, the paper applies the results to approximate solutions of convex minimization problems and presents numerical experiments to demonstrate the efficiency and applicability of the method in comparison with existing methods.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics
Lu-Chuan Ceng, Jen-Chih Yao, Yekini Shehu
Summary: This study investigates numerical methods for hierarchical variational inequalities with the common fixed-point problem constraint in a real Hilbert space, involving a finite family of nonexpansive mappings and an asymptotically nonexpansive mapping. By combining the Mann iteration method with the subgradient extra gradient method and the line-search process, strong convergence results for the sequence of iterates are obtained under suitable assumptions.
Article
Multidisciplinary Sciences
Vasile Berinde
Summary: This paper investigates the approximation of fixed points of enriched nonexpansive mappings in Hilbert spaces and proposes a modified algorithm. Through experiments, it is found that for this class of mappings, the simple fixed point algorithm is more convenient compared to the modified algorithm.
Article
Mathematics, Applied
G. N. Ogwo, C. Izuchukwu, Y. Shehu, O. T. Mewomo
Summary: The paper introduces two new relaxed inertial subgradient extragradient methods for solving variational inequality problems in a real Hilbert space. These methods combine inertial and relaxation techniques to achieve high convergence speed, and experimental results are presented to illustrate the benefits gained from the relaxed inertial steps.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Operations Research & Management Science
Hai Yu, Fenghui Wang
Summary: In this paper, a new relaxed method for solving the split feasibility problem in Hilbert spaces is introduced. The method replaces the projection to the halfspace with the one to the intersection of two halfspaces, and convergence of the sequence generated by this method is proven under certain assumptions. Finally, a numerical example is provided to illustrate the efficiency and implementation of the algorithms in comparison with existing ones in the literature.
Article
Mathematics
Satit Saejung, Rapeepan Kraikaew
Summary: We propose an algorithm that unifies various algorithms for finding a common fixed point of a family of demicontractive mappings and the split common fixed point problem. Furthermore, we improve upon the results of previous works and discuss an algorithm for a class of mappings beyond the scope of previous papers. Lastly, we discuss and enhance the result of a related work in connection with the work of Shehu and Cholamjiak.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2022)
Article
Mathematics
Yun-Ling Cui, Lu-Chuan Ceng, Fang-Fei Zhang, Cong-Shan Wang, Jian-Ye Li, Hui-Ying Hu, Long He
Summary: This paper presents a method for solving the common fixed-point problem and variational inequality problem in a real Hilbert space. By using the Mann iteration method, subgradient extragradient approach, and hybrid deepest-descent technique, two modified rules are constructed and their strong convergence to the solutions of the problems is proven.
Article
Mathematics, Applied
Lu-Chuan Ceng, Jen-Chih Yao, Yekini Shehu
Summary: This article investigates variational inequality problems in a Hilbert space. Two algorithms based on the implicit iteration method and subgradient extragradient method are designed to find common solutions to the problems, with the use of a line-search process. The strong convergence of the algorithms is proved.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2022)
Article
Multidisciplinary Sciences
Lu-Chuan Ceng, Jian-Ye Li, Cong-Shan Wang, Fang-Fei Zhang, Hui-Ying Hu, Yun-Ling Cui, Long He
Summary: In this paper, the concept of alpha-well-posedness is extended to a class of generalized hemivariational inequalities systems, which consist of two symmetric parts. The paper proposes certain concepts and metric characterizations of alpha-well-posedness for generalized hemivariational inequalities systems. Furthermore, equivalence results between the strong alpha-well-posedness of the system of generalized hemivariational inequalities and its system of derived inclusion problems are established.
Article
Mathematics
Yun-Ling Cui, Lu-Chuan Ceng, Fang-Fei Zhang, Cong-Shan Wang, Jian-Ye Li, Hui-Ying Hu, Long He
Summary: This paper presents a method for solving the common fixed-point problem and variational inequality problem in a real Hilbert space. By using the Mann iteration method, subgradient extragradient approach, and hybrid deepest-descent technique, two modified rules are constructed and their strong convergence to the solutions of the problems is proven.
Article
Mathematics, Applied
Lu-Chuan Ceng, Debdas Ghosh, Yekini Shehu, Jen-Chih Yao
Summary: This paper introduces a triple-adaptive subgradient extragradient process with extrapolation to solve a bilevel split pseudomonotone variational inequality problem (BSPVIP) with the common fixed point problem constraint of finitely many nonexpansive mappings. The proposed algorithm exploits the strong monotonicity of one operator at the upper level and the pseudomonotonicity of another mapping at the lower level. The strong convergence result is established under suitable assumptions, and a numerical example is given to demonstrate the viability of the proposed rule.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Lu-Chuan Ceng, Li-Jun Zhu, Tzu-Chien Yin
Summary: This paper introduces a modified algorithm for finding a common solution to a series of problems in a real Hilbert space. The algorithm combines various techniques and approaches, and its strong convergence is proven.
Article
Mathematics, Applied
Lu-chuan Ceng, A. D. R. I. A. N. Petrusel, X. Qin, J. C. Yao
Summary: In this paper, two iterative algorithms are introduced and analyzed for solving the monotone bilevel equilibrium problem (MBEP) with the constraints of GSVI and CFPP, using a new inertial subgradient extragradient rule. Strong convergence theorems for the proposed algorithms are established under mild assumptions. The results of this study improve and extend previous findings in the literature.
FIXED POINT THEORY
(2023)
Article
Mathematics
Yun-Ling Cui, Lu-Chuan Ceng, Fang-Fei Zhang, Liang He, Jie Yin, Cong-Shan Wang, Hui-Ying Hu
Summary: This paper presents a Mann hybrid deepest-descent extragradient approach for solving the hierarchical variational inequality (HVI) problem with the common fixed-point problem (CFPP) and variational inequality problem (VIP) constraints. The proposed algorithms are based on Mann's iterative technique, viscosity approximation method, subgradient extragradient rule with linear-search process, and hybrid deepest-descent rule. It is proved that the sequences constructed by these algorithms strongly converge to a solution of the HVI problem with the CFPP and VIP constraints under suitable restrictions.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Lu-Chuan Ceng, Tzu-Chien Yin
Summary: In this paper, a triple-adaptive inertial subgradient extragradient rule is proposed for solving a bilevel split pseudomonotone variational inequality problem with the common fixed point problem constraint of finitely many nonexpansive mappings in real Hilbert spaces. The rule takes advantage of the strong monotonicity of one operator at the upper-level problem and the pseudomonotonicity of another mapping at the lower level. The strong convergence result for the proposed algorithm is established under suitable assumptions. The results of this paper improve and extend some recent findings.
UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS
(2023)
Article
Mathematics, Applied
Lu-Chuan Ceng, Yeong-Cheng Liou, Tzu-Chien Yin
Summary: In this paper, two Mann-type accelerated projection algorithms with line search method are investigated for solving the pseudomonotone variational inequality (VIP) and the common fixed-point problem (CFPP) in p-uniformly convex and uniformly smooth Banach spaces. Under mild conditions, weak and strong convergence of the proposed algorithms to a common solution of the VIP and CFPP are shown.
Article
Mathematics, Applied
Lu-Chuan Ceng, Tzu-Chien Yin
Summary: This paper introduces a modified viscosity subgradient-like extragradient implicit rule with line-search process for solving a general system of variational inequalities (GSVI) with a variational inequality (VIP) and a fixed-point (FPP) constraints in Hilbert spaces. The suggested algorithms are based on the subgradient extragradient method with line-search process, hybrid Mann implicit iteration method, and composite viscosity approximation method. Under suitable restrictions, the strong convergence of the suggested algorithm to a solution of the GSVI with the VIP and FPP constraints is demonstrated, which is a unique solution of a certain hierarchical variational inequality.
Article
Mathematics, Applied
Lu-Chuan Ceng, Xiaopeng Zhao, Li-jun Zhu
Summary: This paper introduces an algorithm for solving the monotone bilevel equilibrium problem using the general implicit subgradient extragradient method. The algorithm is proven to converge to the desired result under the assumption of monotonicity in the cost functions with Lipschitz-type continuous conditions.
UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS
(2022)
Article
Mathematics
Lu-Chuan Ceng, Li-Jun Zhu, Tzu-Chien Yin
Summary: This article introduces a generalized extragradient implicit method for solving a general system of variational inequalities (GSVI) with the VI and CFPP constraints, and proves the strong convergence of the suggested method under certain assumptions for GSVI problems with the VI and CFPP constraints.
Article
Mathematics, Applied
Lu-Chuan Ceng, Li -Jun Zhu, Zhangsong Yao
Summary: In this paper, two Mann-type implicit inertial sub-gradient extragradient algorithms are introduced and analyzed for solving the monotone bilevel equilibrium problem with a general system of variational inclusions and a common fixed-point problem of a finite family of strict pseudocontraction mappings and an asymptotically nonexpansive mapping constraints. Some strong convergence theorems for the proposed algorithms are established under suitable assumptions.
UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS
(2022)
Article
Mathematics, Applied
L. C. Ceng, S. Y. Cho
Summary: This paper deals with control systems governed by systems of fractional evolution hemivariational inequalities involving Riemann-Liouville fractional derivatives. Suitable sufficient conditions are established to ensure the existence of mild solutions. Under these conditions, the approximate controllability of the associated fractional evolution systems involving Riemann-Liouville fractional derivatives is formulated and proved.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2022)
Article
Mathematics, Applied
Lu-Chuan Ceng, Nan-Jing Huang, Ching-Feng Wen
Summary: In this paper, we investigate a class of generalized global fractional-order composite dynamical systems involving set-valued perturbations in real separable Hilbert spaces. First, we prove that the solution set of the systems is nonempty and closed under some suitable conditions. Second, we show that the solution set is continuous with respect to the initial value in the sense of the Hausdorff metric. Last, an example is provided to illustrate the applicability of the main results.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2022)