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A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings

  • * Corresponding author: Oluwatosin Temitope Mewomo

    * Corresponding author: Oluwatosin Temitope Mewomo

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

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  • In this paper, we present a new modified self-adaptive inertial subgradient extragradient algorithm in which the two projections are made onto some half spaces. Moreover, under mild conditions, we obtain a strong convergence of the sequence generated by our proposed algorithm for approximating a common solution of variational inequality problem and common fixed point of a finite family of demicontractive mappings in a real Hilbert space. The main advantages of our algorithm are: strong convergence result obtained without prior knowledge of the Lipschitz constant of the related monotone operator, the two projections made onto some half-spaces and the inertial technique which speeds up rate of convergence. Finally, we present an application and a numerical example to illustrate the usefulness and applicability of our algorithm.

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


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  • Figure 1.  From Top to Bottom: Case 1 - Case 4

    Table 1.  Numerical results

    Alg. 3.1 Non-inertial
    Case 1 CPU time (sec) 1.9051 2.1221
    No of Iter. 4 6
    Case 2 CPU time (sec) 1.8332 1.9000
    No. of Iter. 4 6
    Case 3 CPU time (sec) 1.9193 2.1708
    No of Iter. 4 6
    Case 4 CPU time (sec) 16.5580 24.9989
    No of Iter. 4 5
     | Show Table
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