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Split Variational Inclusion Problem and Fixed Point Problem for a Class of Multivalued Mappings in CAT (0) Spaces

Author

Listed:
  • Mujahid Abbas

    (Department of Mathematics, Government College University, Lahore 54000, Pakistan
    Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa)

  • Yusuf Ibrahim

    (Department of Mathematics, Sa’adatu Rimi College of Education, Kumbotso Kano, Kano P.M.B. 3218, Nigeria)

  • Abdul Rahim Khan

    (Department of Mathematics and Statistics, King Fahad University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Manuel De la Sen

    (Institute of Research and Development of Processes, University of The Basque Country, Campus of Leioa (Bizkaia), 48080 Leioa, Spain)

Abstract

The aim of this paper is to introduce a modified viscosity iterative method to approximate a solution of the split variational inclusion problem and fixed point problem for a uniformly continuous multivalued total asymptotically strictly pseudocontractive mapping in C A T ( 0 ) spaces. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. Furthermore, we solve a split Hammerstein integral inclusion problem and fixed point problem as an application to validate our result. It seems that our main result in the split variational inclusion problem is new in the setting of C A T ( 0 ) spaces.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:749-:d:258345
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    References listed on IDEAS

    as
    1. 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.
    2. S. S. Chang & L. Wang & Y. K. Tang & L. Yang, 2012. "The Split Common Fixed Point Problem for Total Asymptotically Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, December.
    3. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
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    Cited by:

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