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Viscosity approximation method for solving the multiple-set split equality common fixed-point problems for quasi-pseudocontractive mappings in Hilbert spaces

  • * Corresponding author: Oluwatosin Temitope Mewomo

    * Corresponding author: Oluwatosin Temitope Mewomo
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  • We propose a parallel iterative scheme with viscosity approximation method which converges strongly to a solution of the multiple-set split equality common fixed point problem for quasi-pseudocontractive mappings in real Hilbert spaces. We also give an application of our result to approximation of minimization problem from intensity-modulated radiation therapy. Finally, we present numerical examples to demonstrate the behaviour of our algorithm. This result improves and generalizes many existing results in literature in this direction.

    Mathematics Subject Classification: Primary: 47H10, 47J25; Secondary: 65J15.


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  • Figure 1.  Example 4.3. Top left: Case Ⅰ; Top right: Case Ⅱ; Bottom left: Case Ⅲ; Bottom right: Case Ⅳ

    Figure 2.  Top left: Case IIa; Top right: Case IIb; Bottom left: Case IIc; Bottom right: Case IId

    Figure 3.  Left : Case IIa* Right: Case IIc*

    Table 1.  Numerical result for Example 4.3

    Algorithm 3.2 Algorithm 1.1
    Case Ⅰ No of Iter. 18 44
    CPU time (sec) 7.7529 9.7706
    Case Ⅱ No of Iter. 9 19
    CPU time (sec) 5.2116 8.8849
    Case Ⅲ No of Iter. 10 26
    CPU time (sec) 7.7204 12.7338
    Case Ⅳ No of Iter. 9 22
    CPU time (sec) 5.6424 7.1538
     | Show Table
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    Table 2.  Numerical results

    Alg. (8) Alg. Algorithm 3.2
    Case IIa CPU time (sec) 0.0019 8.8698e-4
    No of Iter. 75 16
    Case IIb CPU time (sec) 0.0020 8.6745e-4
    No. of Iter. 75 16
    Case IIc CPU time (sec) 0.0018 8.5652e-4
    No of Iter. 81 17
    Case IId CPU time (sec) 0.0019 8.9216e-4
    No of Iter. 74 16
     | Show Table
    DownLoad: CSV

    Table 3.  Numerical results

    Alg. (8) Alg. 3.2
    Case IIa* CPU time (sec) 0.0020 8.8533e-4
    No of Iter. 95 17
    Case IIc* CPU time (sec) 0.0021 8.6149e-4
    No of Iter. 103 18
     | Show Table
    DownLoad: CSV
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