IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v218y2024icp498-511.html
   My bibliography  Save this article

Dynamic stepsize iteration process for solving split common fixed point problems with applications

Author

Listed:
  • Kumar, Ajay
  • Thakur, Balwant Singh
  • Postolache, Mihai

Abstract

In this paper, we study the split common fixed point problem for two nonlinear mappings in p-uniformly convex and uniformly smooth Banach spaces. We propose an algorithm which uses dynamic stepsize, it allows to be easily implemented without prior information about operator norm. We further apply our result to solve the split variational inclusion problem, equilibrium problem and convexly constrained linear inverse problem. Moreover, we provide numerical examples to verify efficiency of our algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:218:y:2024:i:c:p:498-511
    DOI: 10.1016/j.matcom.2023.12.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423005128
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.12.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Simeon Reich & Shoham Sabach, 2011. "Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 301-316, Springer.
    3. Li-Wei Kuo & D. R. Sahu, 2013. "Bregman Distance and Strong Convergence of Proximal-Type Algorithms," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, July.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. repec:wsi:jeapmx:v:20:y:2018:i:04:n:s0219198918500056 is not listed on IDEAS
    10. 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.
    11. 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.
    12. 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.
    13. Shipra Singh & Savin Treanţă, 2021. "Characterization results of weak sharp solutions for split variational inequalities with application to traffic analysis," Annals of Operations Research, Springer, vol. 302(1), pages 265-287, July.
    14. Abdellatif Moudafi, 2014. "Computing the resolvent of composite operators," Documents de Travail 2014-02, CEREGMIA, Université des Antilles et de la Guyane.
    15. Le Hai Yen & Le Dung Muu & Nguyen Thi Thanh Huyen, 2016. "An algorithm for a class of split feasibility problems: application to a model in electricity production," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(3), pages 549-565, December.
    16. Yan Tang & Yeol Je Cho, 2019. "Convergence Theorems for Common Solutions of Split Variational Inclusion and Systems of Equilibrium Problems," Mathematics, MDPI, vol. 7(3), pages 1-25, March.
    17. Vahid Darvish, 2016. "Strong convergence theorem for a system of generalized mixed equilibrium problems and finite family of Bregman nonexpansive mappings in Banach spaces," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 584-603, September.
    18. Le Hai Yen & Nguyen Thi Thanh Huyen & Le Dung Muu, 2019. "A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models," Journal of Global Optimization, Springer, vol. 73(4), pages 849-868, April.
    19. Simeon Reich & Truong Minh Tuyen, 2021. "Projection Algorithms for Solving the Split Feasibility Problem with Multiple Output Sets," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 861-878, September.
    20. Jiawei Chen & Zhongping Wan & Liuyang Yuan & Yue Zheng, 2011. "Approximation of Fixed Points of Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-23, July.
    21. Mujahid Abbas & Yusuf Ibrahim & Abdul Rahim Khan & Manuel De la Sen, 2019. "Split Variational Inclusion Problem and Fixed Point Problem for a Class of Multivalued Mappings in CAT (0) Spaces," Mathematics, MDPI, vol. 7(8), pages 1-14, 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:eee:matcom:v:218:y:2024:i:c:p:498-511. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.