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Iterative method for solving split common fixed point problem of asymptotically demicontractive mappings in Hilbert spaces

  • * Corresponding author: Oluwatosin Temitope Mewomo

    * Corresponding author: Oluwatosin Temitope Mewomo

The second author is supported by International Mathematical Union (IMU) Breakout Graduate Fellowship and the third author is supported by National Research Foundation (NRF), South Africa, (Grant Number 119903)

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  • In this paper, we present a new algorithm for solving split common fixed point problem for asymptotically demicontractive mapping in two real Hilbert spaces. Under some mild conditions, we prove that the proposed method converges strongly to a solution of the problem. We give examples to illustrate that the class of asymptotically demicontractive mappings and the class of demicontractive mappings are independent. Moreover, we give numerical experiments to show the efficiency and applicability of our method in comparison with a related method in the literature. The results obtained unify, improve and extend so many related results in the literature in this direction.

    Mathematics Subject Classification: Primary: 65K15, 47J25; Secondary: 65J15.

    Citation:

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  • Figure 1.  Example 4.1: Top left: Case Ⅰ; Top right: Case Ⅱ; Bottom left: Case Ⅲ; Bottom right: Case Ⅳ

    Table 1.  Numerical results for Example 4.1

    Algorithm 3.4 Algorithm (10) Alg. 3.2Chi
    Case I CPU time (sec) 0.0020 0.0024 0.0036
    No. of Iter. 18 21 33
    Case II CPU time (sec) 0.0033 0.0389 0.0054
    No. of Iter. 19 23 35
    Case III CPU time (sec) 0.0026 0.0034 0.0059
    No. of Iter. 18 21 33
    Case IV CPU time (sec) 0.0019 0.0195 0.0032
    No. of Iter. 19 22 34
     | Show Table
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