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
Mathematics
Gaobo Li
Summary: In this paper, two new subgradient extragradient algorithms are introduced to solve a bilevel equilibrium problem in a real Hilbert space, and the weak convergence of the algorithms is proved. Numerical experiments demonstrate the performance of the algorithms.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Anchalee Sripattanet, Atid Kangtunyakarn
Summary: In this paper, we study G-?-strictly pseudocontractive mappings and establish a strong convergence theorem for finding the fixed points of two G-?-strictly pseudocontractive mappings, two G-nonexpansive mappings, and two G-variational inequality problems in a Hilbert space without the Property G. We also prove an interesting result involving the set of fixed points of a G-?-strictly pseudocontractive and G-variational inequality problem, and show that if ? is a G-?-strictly pseudocontractive mapping, then I - ? is a G - ((1-?) )/(2)-inverse strongly monotone mapping in Lemma 3.3. Additionally, we provide some examples to support our main result.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(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
Mathematics, Applied
Jinwei Shi, Yaqin Zheng
Summary: In this paper, a monotone projection method is considered for a finite family of variational inequalities and the problem of fixed points of a strictly pseudocontractive mapping. A strong convergence theorem of common elements in the two solution sets in Hilbert spaces is obtained using nearest point projections, without compact conditions on the space or the mapping.
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2022)
Article
Mathematics, Applied
L. C. Ceng, A. Petrusel, X. Qin, J. C. Yao
Summary: Two new iterative algorithms are introduced for solving a variational inequality problem with pseudomonotone and Lipschitz continuous mapping, and a common fixed-point problem of an asymptotically nonexpansive mapping and a strictly pseudocontractive mapping. Strong convergence of the proposed algorithms in a real Hilbert space is proven under mild conditions.
FIXED POINT THEORY
(2021)
Article
Mathematics
Lu-Chuan Ceng, Ching-Feng Wen, Yeong-Cheng Liou, Jen-Chih Yao
Summary: In this paper, two strengthened inertial-type subgradient extragradient rules are proposed for solving the VIP and CFPP problems, with adaptive step sizes. The strong convergence of these rules to a common solution of the VIP and CFPP, which is the unique solution of a hierarchical variational inequality (HVI), is proved with suitable restrictions.
Article
Mathematics, Applied
Hammed Anuoluwapo Abass, Lateef Olakunle Jolaoso
Summary: The paper proposes a generalized viscosity iterative algorithm for solving multiple-set split feasibility problems and fixed point problems, with the advantage of a self adaptive step size. Strong convergence results are proven for the algorithm, and numerical examples are presented to demonstrate its efficiency and accuracy. The results presented extend and complement recent findings in the literature.
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
Operations Research & Management Science
O. K. Oyewole
Summary: This paper introduces a method for solving variational inequality problems on Hadamard manifolds using a combination of subgradient extragradient and Popov extragradient techniques. Convergence algorithms are proven for pseudomonotone and strongly pseudomonotone cost operators. The method eliminates the dependence on Lipschitz constants of the operators by using a monotone decreasing step size. An application of the method to the constrained convex minimization problem is presented, along with numerical examples to demonstrate its efficiency and applicability.
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
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
Chainarong Khunpanuk, Bancha Panyanak, Nuttapol Pakkaranang
Summary: Two new inertial-type extragradient methods are proposed for solving the variational inequality problem and the fixed point problem. These methods use self-adaptive step size rules and have strong convergence properties under appropriate conditions. Numerical examples demonstrate the effectiveness and validation of the proposed methods.
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
Mathematics, Applied
Araya Kheawborisut, Atid Kangtunyakarn
Summary: This article introduces a modified form of variational inclusion problems, called GSMVIP, and proposes a new subgradient extragradient method for solving it. Strong convergence theorems are proved in a Hilbert space framework, and numerical results indicate the effectiveness of the proposed method.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2021)
Article
Operations Research & Management Science
Dan-Qiong Wang, Tu-Yan Zhao, Lu-Chuan Ceng, Jie Yin, Liang He, Yi-Xuan Fu
Summary: The study introduces a new composite viscosity implicit method for solving the VI and CFPP problems with SVI constraint in uniformly convex and q-uniformly smooth Banach spaces, where strong convergence is achieved. The method is also applicable to various problems in Hilbert spaces.
Article
Mathematics
Lu-Chuan Ceng, Ching-Feng Wen, Yeong-Cheng Liou
Summary: This paper investigates the properties of K-preinvex set-valued maps using the normal subdifferential and equilibrium-like function. It establishes sufficient conditions for the existence of super minimal points of a K-preinvex set-valued map and provides necessary optimality terms for a general type of super efficiency.
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
Safeer Hussain Khan, Abdullah Eqal Al-Mazrooei, Abdul Latif
Summary: The paper introduces the concept of enriched mappings in modular function spaces and studies the enriched ?-contractions and enriched ?-Kannan mappings. Banach Contraction Principle type theorems for the existence of fixed points of such mappings in this setting are established. These results generalize the corresponding results from Banach spaces to modular function spaces and from contractions to enriched ?-contractions. The paper also proves the existence of enriched ?-Kannan mappings, which have not been considered in modular function spaces before. The main results are validated through examples.
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)
