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Weak convergence theorems for symmetric generalized hybrid mappings and equilibrium problems

  • *Corresponding author

    *Corresponding author

This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean Government (NRF-2019R1A2C1008672)

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  • In this paper, we introduce three new iterative methods for finding a common point of the set of fixed points of a symmetric generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Each method can be considered as an combination of Ishikawa's process with the proximal point algorithm, the extragradient algorithm with or without linesearch. Under certain conditions on parameters, the iteration sequences generated by the proposed methods are proved to be weakly convergent to a solution of the problem. These results extend the previous results given in the literature. A numerical example is also provided to illustrate the proposed algorithms.

    Mathematics Subject Classification: 47H06, 47H09, 47H10, 47J05, 47J25.

    Citation:

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  • Table 1.  Results computed with Algorithm 2

    N.P Size (n) Average Times Average Iterations
    10 5 2.3766 152
    10 10 4.2141 223
    10 20 6.7813 457
    10 30 10.5266 515
    10 50 17.4891 567
    10 100 29.2406 674
     | Show Table
    DownLoad: CSV

    Table 2.  Results computed with Algorithm 3

    N.P Size (n) Average Times Average Iterations
    10 5 2.4656 99
    10 10 4.1422 132
    10 20 6.6375 164
    10 30 8.0672 170
    10 50 11.8828 192
    10 100 21.4953 210
     | Show Table
    DownLoad: CSV

    Table 3.  Results computed with Algorithm 1 in [6]

    N.P Size (n) Average Times Average Iterations
    10 5 23.2484 826
    10 10 34.7438 1445
    10 20 87.1016 2346
    10 30 157.5781 2715
    10 50 255.4578 3839
     | Show Table
    DownLoad: CSV

    Table 4.  Results computed with Algorithm 2 in [6]

    N.P Size (n) Average Times Average Iterations
    10 5 38.5938 904
    10 10 106.3172 2242
    10 20 163.1266 3050
    10 30 250.9313 3001
    10 50 359.1094 3592
     | Show Table
    DownLoad: CSV
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