Fixed Point Theory and Applications (Aug 2020)

A hybrid inertial algorithm for approximating solution of convex feasibility problems with applications

  • Charles E. Chidume,
  • Poom Kumam,
  • Abubakar Adamu

DOI
https://doi.org/10.1186/s13663-020-00678-w
Journal volume & issue
Vol. 2020, no. 1
pp. 1 – 17

Abstract

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Abstract An inertial iterative algorithm for approximating a point in the set of zeros of a maximal monotone operator which is also a common fixed point of a countable family of relatively nonexpansive operators is studied. Strong convergence theorem is proved in a uniformly convex and uniformly smooth real Banach space. This theorem extends, generalizes and complements several recent important results. Furthermore, the theorem is applied to convex optimization problems and to J-fixed point problems. Finally, some numerical examples are presented to show the effect of the inertial term in the convergence of the sequence of the algorithm.

Keywords