IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i18p3871-d1237270.html
   My bibliography  Save this article

Novel Multistep Implicit Iterative Methods for Solving Common Solution Problems with Asymptotically Demicontractive Operators and Applications

Author

Listed:
  • Hai-Yang Xu

    (College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China)

  • Heng-You Lan

    (College of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong 643000, China
    South Sichuan Center for Applied Mathematics, Zigong 643000, China)

Abstract

It is very meaningful and challenging to efficiently seek common solutions to operator systems (CSOSs), which are widespread in pure and applied mathematics, as well as some closely related optimization problems. The purpose of this paper is to introduce a novel class of multistep implicit iterative algorithms (MSIIAs) for solving general CSOSs. By using Xu’s lemma and Maingé’s fundamental and important results, we first obtain strong convergence theorems for both one-step and multistep implicit iterative schemes for CSOSs, involving asymptotically demicontractive operators. Finally, for the applications and profits of the main results presented in this paper, we give two numerical examples and present an iterative approximation to solve the general common solution to the variational inequalities and operator equations.

Suggested Citation

  • Hai-Yang Xu & Heng-You Lan, 2023. "Novel Multistep Implicit Iterative Methods for Solving Common Solution Problems with Asymptotically Demicontractive Operators and Applications," Mathematics, MDPI, vol. 11(18), pages 1-20, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3871-:d:1237270
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/18/3871/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/18/3871/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Daron Acemoglu & Ufuk Akcigit & Harun Alp & Nicholas Bloom & William Kerr, 2018. "Innovation, Reallocation, and Growth," American Economic Review, American Economic Association, vol. 108(11), pages 3450-3491, November.
    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. Ufuk Akcigit & Douglas Hanley & Stefanie Stantcheva, 2022. "Optimal Taxation and R&D Policies," Econometrica, Econometric Society, vol. 90(2), pages 645-684, March.
    2. Ufuk Akcigit & Sina T. Ates, 2023. "What Happened to US Business Dynamism?," Journal of Political Economy, University of Chicago Press, vol. 131(8), pages 2059-2124.
    3. Alon, Titan & Berger, David & Dent, Robert & Pugsley, Benjamin, 2018. "Older and slower: The startup deficit’s lasting effects on aggregate productivity growth," Journal of Monetary Economics, Elsevier, vol. 93(C), pages 68-85.
    4. Ufuk Akcigit & Sina T. Ates & Giammario Impullitti, 2018. "Innovation and Trade Policy in a Globalized World," NBER Working Papers 24543, National Bureau of Economic Research, Inc.
    5. Mori, Tomoya & Sakaguchi, Shosei, 2018. "Collaborative knowledge creation: Evidence from Japanese patent data," MPRA Paper 88716, University Library of Munich, Germany.
    6. Aghion, Philippe & Akcigit, Ufuk & Howitt, Peter, 2014. "What Do We Learn From Schumpeterian Growth Theory?," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 0, pages 515-563, Elsevier.
    7. Lin, Jenny X. & Lincoln, William F., 2017. "Pirate's treasure," Journal of International Economics, Elsevier, vol. 109(C), pages 235-245.
    8. Daisuke Miyakawa & Koki Oikawa & Kozo Ueda, 2022. "Reallocation Effects Of Monetary Policy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(2), pages 947-975, May.
    9. Alicia H. Dang & Roberto Samaniego, 2022. "R&D, Industrial Policy and Growth," JRFM, MDPI, vol. 15(8), pages 1-42, August.
    10. Cozzi, Guido & Pataracchia, Beatrice & Pfeiffer, Philipp & Marco, Ratto, 2017. "How much Keynes and how much Schumpeter? An Estimated Macromodel of the US Economy," JRC Working Papers in Economics and Finance 2017-01, Joint Research Centre, European Commission.
    11. John C. Haltiwanger, 2022. "Entrepreneurship during the COVID-19 Pandemic: Evidence from the Business Formation Statistics," Entrepreneurship and Innovation Policy and the Economy, University of Chicago Press, vol. 1(1), pages 9-42.
    12. Jess Benhabib & Jesse Perla & Christopher Tonetti, 2021. "Reconciling Models of Diffusion and Innovation: A Theory of the Productivity Distribution and Technology Frontier," Econometrica, Econometric Society, vol. 89(5), pages 2261-2301, September.
    13. Laurent Cavenaile & Pau Roldan-Blanco, 2021. "Advertising, Innovation, and Economic Growth," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(3), pages 251-303, July.
    14. Acemoglu, Daron & Cao, Dan, 2015. "Innovation by entrants and incumbents," Journal of Economic Theory, Elsevier, vol. 157(C), pages 255-294.
    15. Salome Baslandze, 2015. "The Role of the IT Revolution in Knowledge Diffusion, Innovation and Reallocation," 2015 Meeting Papers 1488, Society for Economic Dynamics.
    16. Jose Asturias & Sewon Hur & Timothy J. Kehoe & Kim J. Ruhl, 2023. "Firm Entry and Exit and Aggregate Growth," American Economic Journal: Macroeconomics, American Economic Association, vol. 15(1), pages 48-105, January.
    17. Chen, You-hua & Chen, Liu-man & Mishra, Ashok K., 2021. "Information, Capacity Constraints and Quality on Firms Competition," 2021 ASAE 10th International Conference (Virtual), January 11-13, Beijing, China 329427, Asian Society of Agricultural Economists (ASAE).
    18. Bryan Hong & Lorenz Kueng & Mu-Jeung Yang, 2015. "Estimating Management Practice Complementarity between Decentralization and Performance Pay," NBER Working Papers 20845, National Bureau of Economic Research, Inc.
    19. Michael Peters & Ufuk Akcigit, 2014. "Lack of Selection and Poor Management Practices: Firm Dynamics in Developing Countries," 2014 Meeting Papers 762, Society for Economic Dynamics.
    20. Coad, Alex & Segarra, Agustí & Teruel, Mercedes, 2016. "Innovation and firm growth: Does firm age play a role?," Research Policy, Elsevier, vol. 45(2), pages 387-400.

    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:11:y:2023:i:18:p:3871-:d:1237270. 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.