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Keywords = quasi-pseudocontractive mapping

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16 pages, 287 KB  
Article
An Averaged Halpern-Type Algorithm for Solving Fixed-Point Problems and Variational Inequality Problems
by Vasile Berinde and Khairul Saleh
Axioms 2024, 13(11), 756; https://doi.org/10.3390/axioms13110756 - 31 Oct 2024
Cited by 1 | Viewed by 1095
Abstract
In this paper, we propose and study an averaged Halpern-type algorithm for approximating the solution of a common fixed-point problem for a couple of nonexpansive and demicontractive mappings with a variational inequality constraint in the setting of a Hilbert space. The strong convergence [...] Read more.
In this paper, we propose and study an averaged Halpern-type algorithm for approximating the solution of a common fixed-point problem for a couple of nonexpansive and demicontractive mappings with a variational inequality constraint in the setting of a Hilbert space. The strong convergence of the sequence generated by the algorithm is established under feasible assumptions on the parameters involved. In particular, we also obtain the common solution of the fixed point problem for nonexpansive or demicontractive mappings and of a variational inequality problem. Our results extend and generalize various important related results in the literature that were established for two pairs of mappings: (nonexpansive, nonspreading) and (nonexpansive, strongly quasi-nonexpansive). Numerical tests to illustrate the superiority of our algorithm over the ones existing in the literature are also reported. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory with Applications)
17 pages, 340 KB  
Article
Novel Accelerated Cyclic Iterative Approximation for Hierarchical Variational Inequalities Constrained by Multiple-Set Split Common Fixed-Point Problems
by Yao Ye and Heng-you Lan
Mathematics 2024, 12(18), 2935; https://doi.org/10.3390/math12182935 - 21 Sep 2024
Viewed by 938
Abstract
In this paper, we investigate a class of hierarchical variational inequalities (HVIPs, i.e., strongly monotone variational inequality problems defined on the solution set of multiple-set split common fixed-point problems) with quasi-pseudocontractive mappings in real Hilbert spaces, with special cases being able to be [...] Read more.
In this paper, we investigate a class of hierarchical variational inequalities (HVIPs, i.e., strongly monotone variational inequality problems defined on the solution set of multiple-set split common fixed-point problems) with quasi-pseudocontractive mappings in real Hilbert spaces, with special cases being able to be found in many important engineering practical applications, such as image recognizing, signal processing, and machine learning. In order to solve HVIPs of potential application value, inspired by the primal-dual algorithm, we propose a novel accelerated cyclic iterative algorithm that combines the inertial method with a correction term and a self-adaptive step-size technique. Our approach eliminates the need for prior knowledge of the bounded linear operator norm. Under appropriate assumptions, we establish strong convergence of the algorithm. Finally, we apply our novel iterative approximation to solve multiple-set split feasibility problems and verify the effectiveness of the proposed iterative algorithm through numerical results. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)
19 pages, 355 KB  
Article
The Split Equality Fixed-Point Problem and Its Applications
by Lawan Bulama Mohammed and Adem Kilicman
Axioms 2024, 13(7), 460; https://doi.org/10.3390/axioms13070460 - 8 Jul 2024
Viewed by 1438
Abstract
It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life. To address this issue, we studied the SEFPP [...] Read more.
It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life. To address this issue, we studied the SEFPP involving a class of quasi-pseudocontractive mappings in Hilbert spaces and constructed novel algorithms in this regard, and we proved the algorithms’ convergences both with and without prior knowledge of the operator norm for bounded and linear mappings. Additionally, we gave applications and numerical examples of our findings. A variety of well-known discoveries revealed in the literature are generalized by the findings presented in this work. Full article
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22 pages, 441 KB  
Article
Approximating a Common Solution of Monotone Inclusion Problems and Fixed Point of Quasi-Pseudocontractive Mappings in CAT(0) Spaces
by Professer Vogani Ndlovu, Lateef Olakunle Jolaoso, Maggie Aphane and Safeer Hussein Khan
Axioms 2022, 11(10), 545; https://doi.org/10.3390/axioms11100545 - 11 Oct 2022
Cited by 1 | Viewed by 1854
Abstract
In this paper, we aimed to introduce a new viscosity-type approximation method for finding the common fixed point of a class of quasi-pseudocontractive mapping and a system of monotone inclusion problems in CAT(0) spaces. We proved some fixed-point properties concerning the class of [...] Read more.
In this paper, we aimed to introduce a new viscosity-type approximation method for finding the common fixed point of a class of quasi-pseudocontractive mapping and a system of monotone inclusion problems in CAT(0) spaces. We proved some fixed-point properties concerning the class of quasi-pseudocontractive mapping in CAT(0) spaces, which is more general than many other mappings such as nonexpansive, quasi-nonexpansive, pseudocontractive and demicontractive mappings which have been studied by other authors. A strong convergence result is proved under some mild conditions on the control sequences and some numerical examples were presented to illustrate the performance and efficiency of the proposed method. Full article
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14 pages, 322 KB  
Article
The Split Equality Fixed Point Problem of Demicontractive Operators with Numerical Example and Application
by Yaqin Wang, Jinzuo Chen and Ariana Pitea
Symmetry 2020, 12(6), 902; https://doi.org/10.3390/sym12060902 - 1 Jun 2020
Cited by 10 | Viewed by 2806
Abstract
This paper aims to propose a new reckoning method for solving the split equality fixed point problem of demicontractive operators in Hilbert spaces, and to establish a theorem with regard to the strong convergence of this new scheme. As an application, we also [...] Read more.
This paper aims to propose a new reckoning method for solving the split equality fixed point problem of demicontractive operators in Hilbert spaces, and to establish a theorem with regard to the strong convergence of this new scheme. As an application, we also consider quasi-pseudo-contractive operators and obtain a result on the solution to the split equality fixed point problem in the framework of Hilbert spaces. A numerical example is also provided. Full article
(This article belongs to the Special Issue Advance in Nonlinear Analysis and Optimization)
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18 pages, 306 KB  
Article
The Split Common Fixed Point Problem for a Family of Multivalued Quasinonexpansive Mappings and Totally Asymptotically Strictly Pseudocontractive Mappings in Banach Spaces
by Ali Abkar, Elahe Shahrosvand and Azizollah Azizi
Mathematics 2017, 5(1), 11; https://doi.org/10.3390/math5010011 - 11 Feb 2017
Cited by 2 | Viewed by 4172
Abstract
In this paper, we introduce an iterative algorithm for solving the split common fixed point problem for a family of multi-valued quasinonexpansive mappings and totally asymptotically strictly pseudocontractive mappings, as well as for a family of totally quasi-ϕ-asymptotically nonexpansive mappings and [...] Read more.
In this paper, we introduce an iterative algorithm for solving the split common fixed point problem for a family of multi-valued quasinonexpansive mappings and totally asymptotically strictly pseudocontractive mappings, as well as for a family of totally quasi-ϕ-asymptotically nonexpansive mappings and k-quasi-strictly pseudocontractive mappings in the setting of Banach spaces. Our results improve and extend the results of Tang et al., Takahashi, Moudafi, Censor et al., and Byrne et al. Full article
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