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Convergence Analysis for Generalized Yosida Inclusion Problem with Applications

Author

Listed:
  • Mohammad Akram

    (Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 42351, Saudi Arabia)

  • Mohammad Dilshad

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 4279, Tabuk 71491, Saudi Arabia)

  • Aysha Khan

    (Department of Mathematics, College of Arts and Science, Wadi-Ad-Dwasir, Prince Sattam Bin Abdulaziz University, Al-Kharj 11991, Saudi Arabia)

  • Sumit Chandok

    (School of Mathematics, Thapar Institute of Engineering & Technology, Patiala 147004, Punjab, India)

  • Izhar Ahmad

    (Department of Mathematics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
    Center for Intelligent Secure Systems, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

Abstract

A new generalized Yosida inclusion problem, involving A -relaxed co-accretive mapping, is introduced. The resolvent and associated generalized Yosida approximation operator is construed and a few of its characteristics are discussed. The existence result is quantified in q -uniformly smooth Banach spaces. A four-step iterative scheme is proposed and its convergence analysis is discussed. Our theoretical assertions are illustrated by a numerical example. In addition, we confirm that the developed method is almost stable for contractions. Further, an equivalent generalized resolvent equation problem is established. Finally, by utilizing the Yosida inclusion problem, we investigate a resolvent equation problem and by employing our proposed method, a Volterra–Fredholm integral equation is examined.

Suggested Citation

  • Mohammad Akram & Mohammad Dilshad & Aysha Khan & Sumit Chandok & Izhar Ahmad, 2023. "Convergence Analysis for Generalized Yosida Inclusion Problem with Applications," Mathematics, MDPI, vol. 11(6), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1409-:d:1097380
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    References listed on IDEAS

    as
    1. S. Takahashi & W. Takahashi & M. Toyoda, 2010. "Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 27-41, October.
    2. Xianghong Lai & Yutian Zhang, 2012. "Fixed Point and Asymptotic Analysis of Cellular Neural Networks," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-12, August.
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