Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems
In this paper, we introduce a new hybrid inertial accelerated algorithm with a line search technique for solving fixed point problems for demimetric mapping and split equilibrium problems in Hilbert spaces. The algorithm is inspired by Tseng’s extragradient method and the viscosity method. Then, we...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/21/2680 |
| _version_ | 1797512110875344896 |
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| author | Yanlai Song |
| author_facet | Yanlai Song |
| author_sort | Yanlai Song |
| collection | DOAJ |
| description | In this paper, we introduce a new hybrid inertial accelerated algorithm with a line search technique for solving fixed point problems for demimetric mapping and split equilibrium problems in Hilbert spaces. The algorithm is inspired by Tseng’s extragradient method and the viscosity method. Then, we establish and prove the strong convergence theorem under proper conditions. Furthermore, we also give a numerical example to support the main results. The main results are new and the proofs are relatively simple and different from those in early and recent literature. |
| first_indexed | 2024-03-10T05:57:16Z |
| format | Article |
| id | doaj.art-dcaf946862034c56b7e5ed28e83d6659 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T05:57:16Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-dcaf946862034c56b7e5ed28e83d66592023-11-22T21:17:15ZengMDPI AGMathematics2227-73902021-10-01921268010.3390/math9212680Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point ProblemsYanlai Song0College of Science, Zhongyuan University of Technology, Zhengzhou 450007, ChinaIn this paper, we introduce a new hybrid inertial accelerated algorithm with a line search technique for solving fixed point problems for demimetric mapping and split equilibrium problems in Hilbert spaces. The algorithm is inspired by Tseng’s extragradient method and the viscosity method. Then, we establish and prove the strong convergence theorem under proper conditions. Furthermore, we also give a numerical example to support the main results. The main results are new and the proofs are relatively simple and different from those in early and recent literature.https://www.mdpi.com/2227-7390/9/21/2680strong convergencesplit equilibrium problemdemimetric mappinghybrid inertial accelerated algorithmsArmijo-like step size rule |
| spellingShingle | Yanlai Song Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems Mathematics strong convergence split equilibrium problem demimetric mapping hybrid inertial accelerated algorithms Armijo-like step size rule |
| title | Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems |
| title_full | Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems |
| title_fullStr | Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems |
| title_full_unstemmed | Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems |
| title_short | Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems |
| title_sort | hybrid inertial accelerated algorithms for solving split equilibrium and fixed point problems |
| topic | strong convergence split equilibrium problem demimetric mapping hybrid inertial accelerated algorithms Armijo-like step size rule |
| url | https://www.mdpi.com/2227-7390/9/21/2680 |
| work_keys_str_mv | AT yanlaisong hybridinertialacceleratedalgorithmsforsolvingsplitequilibriumandfixedpointproblems |