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Split Common Fixed Point Problem of Nonexpansive Semigroup

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Abstract

In this paper, we first introduce a new algorithm with a viscosity iteration method for solving the split common fixed point problem (SCFP) for a finite family of nonexpansive semigroups. We also present a new algorithm for solving the SCFP for an infinite family of quasi-nonexpansive mappings. We establish strong convergence of these algorithms in an infinite-dimensional Hilbert spaces. As application, we obtain strong convergence theorems for split variational inequality problems and split common null point problems. Our results improve and extend the related results in the literature.

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Authors and Affiliations

  1. Department of Mathematics, Mazandaran University of Science and Technology, Behshahr, Iran

    Mohammad Eslamian

  2. Department of Applied Mathematics, Iran University of Science and Technology, Tehran, Iran

    Javad Vahidi

Authors
  1. Mohammad Eslamian
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  2. Javad Vahidi
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Correspondence to Mohammad Eslamian.

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Dedicated to Professor Ghasem Alizadeh Afrouzi on the occasion of his 55th birthday.

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Eslamian, M., Vahidi, J. Split Common Fixed Point Problem of Nonexpansive Semigroup. Mediterr. J. Math. 13, 1177–1195 (2016). https://doi.org/10.1007/s00009-015-0541-3

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  • DOI: https://doi.org/10.1007/s00009-015-0541-3

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