Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces

Yan Tang; Ratthaprom Promkam; Prasit Cholamjiak; Pongsakorn Sunthrayuth

Applications of Mathematics (2022)

  • Volume: 67, Issue: 2, page 129-152
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Tang, Yan, et al. "Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces." Applications of Mathematics 67.2 (2022): 129-152. <http://eudml.org/doc/297688>.

@article{Tang2022,
abstract = {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.},
author = {Tang, Yan, Promkam, Ratthaprom, Cholamjiak, Prasit, Sunthrayuth, Pongsakorn},
journal = {Applications of Mathematics},
keywords = {maximal operator; Bregman distance; reflexive Banach space; weak convergence; strong convergence},
language = {eng},
number = {2},
pages = {129-152},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces},
url = {http://eudml.org/doc/297688},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Tang, Yan
AU - Promkam, Ratthaprom
AU - Cholamjiak, Prasit
AU - Sunthrayuth, Pongsakorn
TI - Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 2
SP - 129
EP - 152
AB - 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.
LA - eng
KW - maximal operator; Bregman distance; reflexive Banach space; weak convergence; strong convergence
UR - http://eudml.org/doc/297688
ER -

References

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