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Approximation of the Solution of Split Equality Fixed Point Problem for Family of Multivalued Demicontractive Operators with Application

Author

Listed:
  • Ismat Beg

    (Department of Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 54000, Pakistan)

  • Mujahid Abbas

    (Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
    Department of Medical Research, China Medical University, Taichung 404, Taiwan)

  • Muhammad Waseem Asghar

    (Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan)

Abstract

In this paper, a new viscosity type iterative algorithm is used for obtaining a strong convergence result of split equality fixed point solutions for infinite families of multivalued demicontractive mappings in real Hilbert spaces. Our iterative scheme is based on choosing the step-sizes without calculating or estimating the operator norms and the condition of hemicompactness was relaxed to prove the strong convergence result. As an application, the solution of split convex minimization problem was approximated. The result presented herein unifies and extends several comparable results in the literature.

Suggested Citation

  • Ismat Beg & Mujahid Abbas & Muhammad Waseem Asghar, 2023. "Approximation of the Solution of Split Equality Fixed Point Problem for Family of Multivalued Demicontractive Operators with Application," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:959-:d:1067125
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    References listed on IDEAS

    as
    1. Boikanyo, Oganeditse A., 2015. "A strongly convergent algorithm for the split common fixed point problem," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 844-853.
    2. Andrzej Cegielski, 2015. "General Method for Solving the Split Common Fixed Point Problem," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 385-404, May.
    3. Charles L. Byrne and Abdellatif Moudafi, 2013. "Extensions of the CQ Algorithm for the Split Feasibility and Split Equality Problems," Documents de Travail 2013-01, CEREGMIA, Université des Antilles et de la Guyane.
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