Geodesic
Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces
Applications of Mathematics, Tome 67 (2022) no. 2, pp. 129-152 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The aim of this paper is to propose two modified forward-backward splitting algorithms for zeros of the sum of a maximal monotone operator and a Bregman inverse strongly monotone operator in reflexive Banach spaces. We prove weak and strong convergence theorems of the generated sequences by the proposed methods under some suitable conditions. We apply our results to study the variational inequality problem and the equilibrium problem. Finally, a numerical example is given to illustrate the proposed methods. The results presented in this paper improve and generalize many known results in recent literature.
The aim of this paper is to propose two modified forward-backward splitting algorithms for zeros of the sum of a maximal monotone operator and a Bregman inverse strongly monotone operator in reflexive Banach spaces. We prove weak and strong convergence theorems of the generated sequences by the proposed methods under some suitable conditions. We apply our results to study the variational inequality problem and the equilibrium problem. Finally, a numerical example is given to illustrate the proposed methods. The results presented in this paper improve and generalize many known results in recent literature.
DOI : 10.21136/AM.2021.0108-20
Classification : 47H05, 47H09, 47H10, 47J05, 47J25
Keywords: maximal operator; Bregman distance; reflexive Banach space; weak convergence; strong convergence 
@article{10_21136_AM_2021_0108_20,
     author = {Tang, Yan and Promkam, Ratthaprom and Cholamjiak, Prasit and Sunthrayuth, Pongsakorn},
     title = {Convergence results of iterative algorithms for the sum of two monotone operators in reflexive {Banach} spaces},
     journal = {Applications of Mathematics},
     pages = {129--152},
     year = {2022},
     volume = {67},
     number = {2},
     doi = {10.21136/AM.2021.0108-20},
     mrnumber = {4396681},
     zbl = {07511498},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0108-20/}
}
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Tang, Yan; Promkam, Ratthaprom; Cholamjiak, Prasit; Sunthrayuth, Pongsakorn. Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces. Applications of Mathematics, Tome 67 (2022) no. 2, pp. 129-152. doi: 10.21136/AM.2021.0108-20

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