Generalized relaxed inertial method with regularization for solving split feasibility problems in real Hilbert spaces

A. A. Mebawondu*, L. O. Jolaoso, H. A. Abass, O. K. Narain

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we propose a new modified relaxed inertial regularization method for finding a common solution of a generalized split feasibility problem, the zeros of sum of maximal monotone operators, and fixed point problem of two nonlinear mappings in real Hilbert spaces. We prove that the proposed method converges strongly to a minimum-norm solution of the aforementioned problems without using the conventional two cases approach. In addition, we apply our convergence results to the classical variational inequality and equilibrium problems, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other existing methods in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

Original languageEnglish
Article number2250106
JournalAsian-European Journal of Mathematics
DOIs
Publication statusAccepted/In press - 2021
Externally publishedYes

Keywords

  • Regularization method
  • firmly nonexpansive
  • fixed point problem
  • inertial iterative scheme
  • split feasibility problem

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