An Inertial Subgradient Extragradient Method for Efficiently Solving Fixed-Point and Equilibrium Problems in Infinite Families of Demimetric Mappings
The primary objective of this article is to enhance the convergence rate of the extragradient method through the careful selection of inertial parameters and the design of a self-adaptive stepsize scheme. We propose an improved version of the extragradient method for approximating a common solution...
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2024-12-01
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| Series: | Mathematics |
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| author | Habib ur Rehman Fouzia Amir Jehad Alzabut Mohammad Athar Azim |
| author_facet | Habib ur Rehman Fouzia Amir Jehad Alzabut Mohammad Athar Azim |
| author_sort | Habib ur Rehman |
| collection | DOAJ |
| description | The primary objective of this article is to enhance the convergence rate of the extragradient method through the careful selection of inertial parameters and the design of a self-adaptive stepsize scheme. We propose an improved version of the extragradient method for approximating a common solution to pseudomonotone equilibrium and fixed-point problems that involve an infinite family of demimetric mappings in real Hilbert spaces. We establish that the iterative sequences generated by our proposed algorithms converge strongly under suitable conditions. These results substantiate the effectiveness of our approach in achieving convergence, marking a significant advancement in the extragradient method. Furthermore, we present several numerical tests to illustrate the practical efficiency of the proposed method, comparing these results with those from established methods to demonstrate the improved convergence rates and solution accuracy achieved through our approach. |
| format | Article |
| id | doaj-art-97b6cc036b924a05b1b75dba615f3138 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-97b6cc036b924a05b1b75dba615f31382025-01-10T13:17:59ZengMDPI AGMathematics2227-73902024-12-011312010.3390/math13010020An Inertial Subgradient Extragradient Method for Efficiently Solving Fixed-Point and Equilibrium Problems in Infinite Families of Demimetric MappingsHabib ur Rehman0Fouzia Amir1Jehad Alzabut2Mohammad Athar Azim3School of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaCenter for Research and Innovation, Asia International University, Bukhara 200100, UzbekistanDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaPreparatory Year Programme, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaThe primary objective of this article is to enhance the convergence rate of the extragradient method through the careful selection of inertial parameters and the design of a self-adaptive stepsize scheme. We propose an improved version of the extragradient method for approximating a common solution to pseudomonotone equilibrium and fixed-point problems that involve an infinite family of demimetric mappings in real Hilbert spaces. We establish that the iterative sequences generated by our proposed algorithms converge strongly under suitable conditions. These results substantiate the effectiveness of our approach in achieving convergence, marking a significant advancement in the extragradient method. Furthermore, we present several numerical tests to illustrate the practical efficiency of the proposed method, comparing these results with those from established methods to demonstrate the improved convergence rates and solution accuracy achieved through our approach.https://www.mdpi.com/2227-7390/13/1/20equilibrium problemspseudomonotone bifunctionextragradient methodstrongly pseudomonotone bifunctionstrong convergence |
| spellingShingle | Habib ur Rehman Fouzia Amir Jehad Alzabut Mohammad Athar Azim An Inertial Subgradient Extragradient Method for Efficiently Solving Fixed-Point and Equilibrium Problems in Infinite Families of Demimetric Mappings Mathematics equilibrium problems pseudomonotone bifunction extragradient method strongly pseudomonotone bifunction strong convergence |
| title | An Inertial Subgradient Extragradient Method for Efficiently Solving Fixed-Point and Equilibrium Problems in Infinite Families of Demimetric Mappings |
| title_full | An Inertial Subgradient Extragradient Method for Efficiently Solving Fixed-Point and Equilibrium Problems in Infinite Families of Demimetric Mappings |
| title_fullStr | An Inertial Subgradient Extragradient Method for Efficiently Solving Fixed-Point and Equilibrium Problems in Infinite Families of Demimetric Mappings |
| title_full_unstemmed | An Inertial Subgradient Extragradient Method for Efficiently Solving Fixed-Point and Equilibrium Problems in Infinite Families of Demimetric Mappings |
| title_short | An Inertial Subgradient Extragradient Method for Efficiently Solving Fixed-Point and Equilibrium Problems in Infinite Families of Demimetric Mappings |
| title_sort | inertial subgradient extragradient method for efficiently solving fixed point and equilibrium problems in infinite families of demimetric mappings |
| topic | equilibrium problems pseudomonotone bifunction extragradient method strongly pseudomonotone bifunction strong convergence |
| url | https://www.mdpi.com/2227-7390/13/1/20 |
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