Forward-backward splitting algorithm with self-adaptive method for finite family of split minimization and fixed point problems in Hilbert spaces

Authors

  • Hammed Anuoluwapo Abbas Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Science University, Ga-Rankuwa, South Africa https://orcid.org/0000-0002-4236-3278
  • Kazeem Aremu Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Science University, Ga-Rankuwa, South Africa
  • Olawale Oyewole School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
  • Akindele Mebawondu Department of Computer Science and Mathematics, Mountain Top University, Prayer City, Nigeria
  • Ojen Narain School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

DOI:

https://doi.org/10.33993/jnaat522-1351

Keywords:

Nonexpansive mapping, minimization problem, inertial method, forward-backward splitting method, fixed point problem
Abstract views: 117

Abstract

In this paper, we introduce an inertial forward-backward splitting method together with a Halpern iterative algorithm for approximating a common solution of a finite family of split minimization problem involving two proper, lower semicontinuous and convex functions and fixed point problem of a nonexpansive mapping in real Hilbert spaces. Under suitable conditions, we proved that the sequence generated by our algorithm converges strongly to a solution of the aforementioned problems. The stepsizes studied in this paper are designed in such a way that they do not require the Lipschitz continuity condition on the gradient and prior knowledge of operator norm. Finally, we illustrate a numerical experiment to show the performance of the proposed method. The result discussed in this paper extends and complements many related results in literature.

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References

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Published

2023-12-28

How to Cite

Abbas, H. A., Aremu, K., Oyewole, O., Mebawondu, A., & Narain, O. (2023). Forward-backward splitting algorithm with self-adaptive method for finite family of split minimization and fixed point problems in Hilbert spaces. J. Numer. Anal. Approx. Theory, 52(2), 109–127. https://doi.org/10.33993/jnaat522-1351

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