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Equivalence of Certain Iteration Processes Obtained by Two New Classes of Operators

Author

Listed:
  • Mujahid Abbas

    (Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    These authors contributed equally to this work.)

  • Rizwan Anjum

    (Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
    These authors contributed equally to this work.)

  • Vasile Berinde

    (Department of Mathematics and Computer Science, North University Center at Baia Mare, Technical University of Cluj-Napoca, Victoriei 76, 430122 Baia Mare, Romania
    Academy of Romanian Scientists, Ilfov Str. No. 3, 50044 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

The aim of this paper is two fold: the first is to define two new classes of mappings and show the existence and iterative approximation of their fixed points; the second is to show that the Ishikawa, Mann, and Krasnoselskij iteration methods defined for such classes of mappings are equivalent. An application of the main results to solve split feasibility and variational inequality problems are also given.

Suggested Citation

  • Mujahid Abbas & Rizwan Anjum & Vasile Berinde, 2021. "Equivalence of Certain Iteration Processes Obtained by Two New Classes of Operators," Mathematics, MDPI, vol. 9(18), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2292-:d:637518
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    References listed on IDEAS

    as
    1. B. E. Rhoades & Ştefan M. Şoltuz, 2003. "The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-7, January.
    2. B. E. Rhoades & Stefan M. Soltuz, 2003. "On the equivalence of Mann and Ishikawa iteration methods," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-9, January.
    Full references (including those not matched with items on IDEAS)

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