An inertial generalized viscosity approximation method for solving multiple-sets split feasibility problems and common fixed point of strictly pseudo-nonspreading mappings

Hammed Anuoluwapo Abass, Lateef Olakunle Jolaoso*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper, we propose a generalized viscosity iterative algorithm which includes a sequence of contractions and a self adaptive step size for approximating a common solution of a multiple-set split feasibility problem and fixed point problem for countable families of k-strictly pseudononspeading mappings in the framework of real Hilbert spaces. The advantage of the step size introduced in our algorithm is that it does not require the computation of the Lipschitz constant of the gradient operator which is very difficult in practice. We also introduce an inertial process version of the generalize viscosity approximation method with self adaptive step size. We prove strong convergence results for the sequences generated by the algorithms for solving the aforementioned problems and present some numerical examples to show the efficiency and accuracy of our algorithm. The results presented in this paper extends and complements many recent results in the literature.

Original languageEnglish
Article number1
Pages (from-to)1-18
Number of pages18
JournalAxioms
Volume10
Issue number1
DOIs
Publication statusPublished - Mar 2021

Keywords

  • Fixed point problem
  • Multiple-sets split feasibility problem
  • Nonexpan-sive mappings
  • Strictly pseudocontractive mappings
  • Viscossity iterative scheme

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