IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i12p2098-d840675.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/12/2098/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/10/12/2098/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yonghong Yao & Yeong-Cheng Liou & Ngai-Ching Wong, 2013. "Superimposed optimization methods for the mixed equilibrium problem and variational inclusion," Journal of Global Optimization, Springer, vol. 57(3), pages 935-950, November.
    2. Marwan A. Kutbi & Abdul Latif & Xiaolong Qin, 2019. "Convergence of Two Splitting Projection Algorithms in Hilbert Spaces," Mathematics, MDPI, vol. 7(10), pages 1-13, October.
    3. Pawicha Phairatchatniyom & Poom Kumam & Yeol Je Cho & Wachirapong Jirakitpuwapat & Kanokwan Sitthithakerngkiet, 2019. "The Modified Inertial Iterative Algorithm for Solving Split Variational Inclusion Problem for Multi-Valued Quasi Nonexpansive Mappings with Some Applications," Mathematics, MDPI, vol. 7(6), pages 1-22, June.
    4. Suthep Suantai & Suparat Kesornprom & Prasit Cholamjiak, 2019. "Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions," Mathematics, MDPI, vol. 7(8), pages 1-17, August.
    5. Fabiana R. Oliveira & Orizon P. Ferreira & Gilson N. Silva, 2019. "Newton’s method with feasible inexact projections for solving constrained generalized equations," Computational Optimization and Applications, Springer, vol. 72(1), pages 159-177, January.
    6. Sitthithakerngkiet, Kanokwan & Deepho, Jitsupa & Kumam, Poom, 2015. "A hybrid viscosity algorithm via modify the hybrid steepest descent method for solving the split variational inclusion in image reconstruction and fixed point problems," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 986-1001.
    7. 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.
    8. Thidaporn Seangwattana & Somyot Plubtieng & Kanokwan Sitthithakerngkiet, 2021. "A new linesearch iterative scheme for finding a common solution of split equilibrium and fixed point problems," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 614-628, June.
    9. Bunyawee Chaloemyotphong & Atid Kangtunyakarn, 2019. "Modified Halpern Iterative Method for Solving Hierarchical Problem and Split Combination of Variational Inclusion Problem in Hilbert Space," Mathematics, MDPI, vol. 7(11), pages 1-26, November.
    10. Hasanen A. Hammad & Habib ur Rehman & Manuel De la Sen, 2022. "A New Four-Step Iterative Procedure for Approximating Fixed Points with Application to 2D Volterra Integral Equations," Mathematics, MDPI, vol. 10(22), pages 1-26, November.
    11. Liya Liu & Xiaolong Qin & Jen-Chih Yao, 2020. "A Hybrid Forward–Backward Algorithm and Its Optimization Application," Mathematics, MDPI, vol. 8(3), pages 1-16, March.
    12. Prasit Cholamjiak & Suparat Kesornprom & Nattawut Pholasa, 2019. "Weak and Strong Convergence Theorems for the Inclusion Problem and the Fixed-Point Problem of Nonexpansive Mappings," Mathematics, MDPI, vol. 7(2), pages 1-19, February.
    13. Kim, Jong Kyu & Tuyen, Truong Minh, 2016. "Approximation common zero of two accretive operators in banach spaces," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 265-281.
    14. W. Takahashi, 2013. "Strong Convergence Theorems for Maximal and Inverse-Strongly Monotone Mappings in Hilbert Spaces and Applications," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 781-802, June.
    15. Pingjing Xia & Gang Cai & Qiao-Li Dong, 2023. "A Strongly Convergent Viscosity-Type Inertial Algorithm with Self Adaptive Stepsize for Solving Split Variational Inclusion Problems in Hilbert Spaces," Networks and Spatial Economics, Springer, vol. 23(4), pages 931-952, December.
    16. Wataru Takahashi, 2020. "A Strong Convergence Theorem under a New Shrinking Projection Method for Finite Families of Nonlinear Mappings in a Hilbert Space," Mathematics, MDPI, vol. 8(3), pages 1-15, March.
    17. repec:wsi:jeapmx:v:20:y:2018:i:04:n:s0219198918500056 is not listed on IDEAS
    18. Che, Haitao & Li, Meixia, 2016. "The conjugate gradient method for split variational inclusion and constrained convex minimization problems," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 426-438.
    19. Shih-sen Chang & Jen-Chih Yao & Ching-Feng Wen & Liang-cai Zhao, 2020. "On the Split Equality Fixed Point Problem of Quasi-Pseudo-Contractive Mappings Without A Priori Knowledge of Operator Norms with Applications," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 343-360, May.
    20. Kumar, Ajay & Thakur, Balwant Singh & Postolache, Mihai, 2024. "Dynamic stepsize iteration process for solving split common fixed point problems with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 498-511.
    21. Shih-sen Chang & Lin Wang & Xiong Rui Wang & Gang Wang, 2015. "General Split Equality Equilibrium Problems with Application to Split Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 377-390, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2098-:d:840675. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.