IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i4p372-d498667.html
   My bibliography  Save this article

A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

Author

Listed:
  • Nishu Gupta

    (Department of Mathematics, Pt NRS Government College, Rohtak 124001, India
    These authors contributed equally to this work.)

  • Mihai Postolache

    (Department of General Education, China Medical University, Taichung 40402, Taiwan
    Department of Interior Design, Asia University, Taichung 41354, Taiwan
    Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania
    Department of Mathematics and Informatics, University “Politehnica” of Bucharest, 060042 Bucharest, Romania)

  • Ashish Nandal

    (Government College, Bhainswal Kalan 131001, India
    These authors contributed equally to this work.)

  • Renu Chugh

    (Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, India
    These authors contributed equally to this work.)

Abstract

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

Suggested Citation

  • Nishu Gupta & Mihai Postolache & Ashish Nandal & Renu Chugh, 2021. "A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm," Mathematics, MDPI, vol. 9(4), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:372-:d:498667
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/4/372/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/4/372/
    Download Restriction: no
    ---><---

    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. 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. Biban, Geeta & Chugh, Renu & Panwar, Anju, 2023. "Image encryption based on 8D hyperchaotic system using Fibonacci Q-Matrix," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Yao Ye & Heng-you Lan, 2024. "Novel Accelerated Cyclic Iterative Approximation for Hierarchical Variational Inequalities Constrained by Multiple-Set Split Common Fixed-Point Problems," Mathematics, MDPI, vol. 12(18), pages 1-17, September.
    3. Maliha Rashid & Amna Kalsoom & Amer Hassan Albargi & Aftab Hussain & Hira Sundas, 2024. "Convergence Result for Solving the Split Fixed Point Problem with Multiple Output Sets in Nonlinear Spaces," Mathematics, MDPI, vol. 12(12), pages 1-20, June.
    4. Li-Jun Zhu & Yonghong Yao, 2023. "Algorithms for Approximating Solutions of Split Variational Inclusion and Fixed-Point Problems," Mathematics, MDPI, vol. 11(3), pages 1-12, January.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Nattakarn Kaewyong & Kanokwan Sitthithakerngkiet, 2022. "An Inertial Extragradient Direction Method with Self-Adaptive Step Size for Solving Split Minimization Problems and Its Applications to Compressed Sensing," Mathematics, MDPI, vol. 10(6), pages 1-25, March.
    7. Abdellatif Moudafi, 2014. "Computing the resolvent of composite operators," Documents de Travail 2014-02, CEREGMIA, Université des Antilles et de la Guyane.
    8. 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.
    9. Truong Minh Tuyen & Nguyen Thi Thu Thuy & Nguyen Minh Trang, 2019. "A Strong Convergence Theorem for a Parallel Iterative Method for Solving the Split Common Null Point Problem in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 183(1), pages 271-291, October.
    10. Andreea Bejenaru & Mihai Postolache, 2022. "New Approach to Split Variational Inclusion Issues through a Three-Step Iterative Process," Mathematics, MDPI, vol. 10(19), pages 1-16, October.
    11. Suthep Suantai & Narin Petrot & Manatchanok Khonchaliew, 2021. "Inertial Extragradient Methods for Solving Split Equilibrium Problems," Mathematics, MDPI, vol. 9(16), pages 1-18, August.
    12. 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.
    13. Ali Abkar & Elahe Shahrosvand & Azizollah Azizi, 2017. "The Split Common Fixed Point Problem for a Family of Multivalued Quasinonexpansive Mappings and Totally Asymptotically Strictly Pseudocontractive Mappings in Banach Spaces," Mathematics, MDPI, vol. 5(1), pages 1-18, February.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Soumitra Dey & Chinedu Izuchukwu & Adeolu Taiwo & Simeon Reich, 2025. "New iterative algorithms for solving split variational inclusions," Journal of Global Optimization, Springer, vol. 91(3), pages 587-609, March.
    19. Wachirapong Jirakitpuwapat & Poom Kumam & Yeol Je Cho & Kanokwan Sitthithakerngkiet, 2019. "A General Algorithm for the Split Common Fixed Point Problem with Its Applications to Signal Processing," Mathematics, MDPI, vol. 7(3), pages 1-20, February.
    20. repec:wsi:jeapmx:v:20:y:2018:i:04:n:s0219198918500056 is not listed on IDEAS
    21. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:9:y:2021:i:4:p:372-:d:498667. 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.