Mathematics (Mar 2024)

Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem

  • Ahmed Alamer,
  • Mohammad Dilshad

DOI
https://doi.org/10.3390/math12050747
Journal volume & issue
Vol. 12, no. 5
p. 747

Abstract

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In this paper, two Halpern-type inertial iteration methods with self-adaptive step size are proposed for estimating the solution of split common null point problems (SpCNPP) in such a way that the Halpern iteration and inertial extrapolation are computed simultaneously in the beginning of each iteration. We prove the strong convergence of sequences driven by the suggested methods without estimating the norm of bounded linear operator when certain appropriate assumptions are made. We demonstrate the efficiency of our iterative methods and compare them with some related and well-known results using relevant numerical examples.

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