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Advances in Fixed Point Theory ISSN 1927-6303 (Print)

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Adv. Fixed Point Theory 12 (2022), Article ID 6

Inexact generalized proximal point algorithm with alternating inertial steps for monotone inclusion problem

J. N. Ezeora, F. E. Bazuaye

PDF (169.5 KB) https://doi.org/10.28919/afpt/7065

Abstract

In this paper, we propose and study an inexact generalized proximal point algorithm with alternated inertial steps for solving monotone inclusion problem and obtain weak convergence results under some mild conditions. In the case when the operator T is such that T-1 is Lipschitz continuous at 0, we prove that the sequence of the iterates is linearly convergent. Fejer monotonicity of even subsequences of the iterates is also obtained. Finally, we give some priori and posteriori error estimates of our generated sequences.

Published
30 March 2022
Volume
12 (2022)
License
CC BY 3.0

Copyright © 2022 J. N. Ezeora, F. E. Bazuaye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

J. N. Ezeora, F. E. Bazuaye, Inexact generalized proximal point algorithm with alternating inertial steps for monotone inclusion problem, Adv. Fixed Point Theory 12 (2022), 6. https://doi.org/10.28919/afpt/7065

BibTeX
@article{Ezeora2022,
  author  = {Ezeora, J. N. and Bazuaye, F. E.},
  title   = {Inexact generalized proximal point algorithm with alternating inertial steps for monotone inclusion problem},
  journal = {Adv. Fixed Point Theory},
  volume  = {12},
  year    = {2022},
  pages   = {6},
  doi     = {10.28919/afpt/7065}
}