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Modified Iterative Schemes for a Fixed Point Problem and a Split Variational Inclusion Problem

Author

Listed:
  • Mohammad Akram

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

  • Mohammad Dilshad

    (Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Arvind Kumar Rajpoot

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Feeroz Babu

    (Department of Applied Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Rais Ahmad

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Jen-Chih Yao

    (Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

Abstract

In this paper, we alter Wang’s new iterative method as well as apply it to find the common solution of fixed point problem (FPP) and split variational inclusion problem ( S p VIP) in Hilbert space. We discuss the weak convergence for ( S p VIP) and strong convergence for the common solution of ( S p VIP) and (FPP) using appropriate assumptions. Some consequences of the proposed methods are studied. We compare our iterative schemes with other existing related schemes.

Suggested Citation

  • Mohammad Akram & Mohammad Dilshad & Arvind Kumar Rajpoot & Feeroz Babu & Rais Ahmad & Jen-Chih Yao, 2022. "Modified Iterative Schemes for a Fixed Point Problem and a Split Variational Inclusion Problem," Mathematics, MDPI, vol. 10(12), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2098-:d:840675
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    References listed on IDEAS

    as
    1. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    2. Hasanen A. Hammad & Habib ur Rehman & Manuel De la Sen, 2020. "Shrinking Projection Methods for Accelerating Relaxed Inertial Tseng-Type Algorithm with Applications," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-14, November.
    3. 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.
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    Cited by:

    1. Mohd Asad & Mohammad Dilshad & Doaa Filali & Mohammad Akram, 2023. "A Modified Viscosity-Type Self-Adaptive Iterative Algorithm for Common Solution of Split Problems with Multiple Output Sets in Hilbert Spaces," Mathematics, MDPI, vol. 11(19), pages 1-18, October.
    2. Ahmed Alamer & Mohammad Dilshad, 2024. "Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem," Mathematics, MDPI, vol. 12(5), pages 1-16, March.
    3. Kasamsuk Ungchittrakool & Somyot Plubtieng & Natthaphon Artsawang & Purit Thammasiri, 2023. "Modified Mann-Type Algorithm for Two Countable Families of Nonexpansive Mappings and Application to Monotone Inclusion and Image Restoration Problems," Mathematics, MDPI, vol. 11(13), pages 1-21, June.

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