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Iterative algorithms for solutions of Hammerstein integral inclusions

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  • Minjibir, M.S.
  • Mohammed, I.

Abstract

Let H be a real Hilbert space and let F: H → 2H, K: H → H be maps such that F(x) is closed bounded and nonempty for each x ∈ H. Assuming K and F are monotone, bounded and continuous (relative to the Hausdorff metric in case of F) having full domain, an iterative process is constructed and the sequence of the process is proved to converge strongly to a solution of the Hammerstein inclusion 0∈u+KFu, provided a solution exists. The process does not require invertibility of K. This work generalizes established results from singlevalued setting to multivalued one.

Suggested Citation

  • Minjibir, M.S. & Mohammed, I., 2018. "Iterative algorithms for solutions of Hammerstein integral inclusions," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 389-399.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:389-399
    DOI: 10.1016/j.amc.2017.09.041
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    References listed on IDEAS

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    1. Mishra, Lakshmi Narayan & Sen, Mausumi, 2016. "On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 174-183.
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    Cited by:

    1. Mujahid Abbas & Yusuf Ibrahim & Abdul Rahim Khan & Manuel De la Sen, 2019. "Split Variational Inclusion Problem and Fixed Point Problem for a Class of Multivalued Mappings in CAT (0) Spaces," Mathematics, MDPI, vol. 7(8), pages 1-14, August.

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