IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i18p2877-d1478821.html
   My bibliography  Save this article

Fixed-Point and Random Fixed-Point Theorems in Preordered Sets Equipped with a Distance Metric

Author

Listed:
  • Himanshu Baranwal

    (Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India)

  • Ravindra Kishor Bisht

    (Department of Mathematics, National Defence Academy, Pune 411023, India)

  • Arya Kumar Bedabrata Chand

    (Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India)

  • Jen-Chih Yao

    (Center for General Education, China Medical University, Taichung 40402, Taiwan
    UNEC Mathematical Modeling and Optimization Research Center, Azerbaijan State University of Economics (UNEC), Istiqlaliyyat Str. 6, Baku 1001, Azerbaijan)

Abstract

This paper explores fixed points for both contractive and non-contractive mappings in traditional b -metric spaces, preordered b -metric spaces, and random b -metric spaces. Our findings provide insights into the behavior of mappings under various constraints and extend our approach to include coincidence and common fixed-point theorems in these spaces. We present new examples and graphical representations for the first time, offering novel results and enhancing several related findings in the literature, while broadening the scope of earlier works of Ran and Reurings, Nieto and Rodríguez-López, Górnicki, and others.

Suggested Citation

  • Himanshu Baranwal & Ravindra Kishor Bisht & Arya Kumar Bedabrata Chand & Jen-Chih Yao, 2024. "Fixed-Point and Random Fixed-Point Theorems in Preordered Sets Equipped with a Distance Metric," Mathematics, MDPI, vol. 12(18), pages 1-30, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2877-:d:1478821
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/18/2877/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/18/2877/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. H.K. Xu, 2003. "An Iterative Approach to Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 116(3), pages 659-678, March.
    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. Rattanaporn Wangkeeree & Rabian Wangkeeree, 2013. "The general iterative methods for nonexpansive semigroups in Banach spaces," Journal of Global Optimization, Springer, vol. 55(2), pages 417-436, February.
    2. 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.
    3. Shengquan Weng & Dingping Wu, 2018. "Convergence Theorems of Modified Proximal Algorithms for Asymptotical Quasi-nonexpansive Mappings in CAT(0) Spaces," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(2), pages 66-76, April.
    4. Mohammad Eslamian & Ali Abkar, 2014. "Viscosity iterative scheme for generalized mixed equilibrium problems and nonexpansive semigroups," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 554-570, July.
    5. F. Cianciaruso & G. Marino & L. Muglia, 2010. "Iterative Methods for Equilibrium and Fixed Point Problems for Nonexpansive Semigroups in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 491-509, August.
    6. Atid Kangtunyakarn, 2013. "A new iterative scheme for fixed point problems of infinite family of κ i -pseudo contractive mappings, equilibrium problem, variational inequality problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1543-1562, August.
    7. 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.
    8. Eric U. Ofoedu, 2013. "A General Approximation Scheme for Solutions of Various Problems in Fixed Point Theory," International Journal of Analysis, Hindawi, vol. 2013, pages 1-18, January.
    9. Uthai Kamraksa & Rabian Wangkeeree, 2011. "Generalized equilibrium problems and fixed point problems for nonexpansive semigroups in Hilbert spaces," Journal of Global Optimization, Springer, vol. 51(4), pages 689-714, December.
    10. Giuseppe Marino & Hong-Kun Xu, 2011. "Explicit Hierarchical Fixed Point Approach to Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 61-78, April.
    11. L. C. Zeng & N. C. Wong & J. C. Yao, 2007. "Convergence Analysis of Modified Hybrid Steepest-Descent Methods with Variable Parameters for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 132(1), pages 51-69, January.
    12. S. Saeidi & D. S. Kim, 2014. "Combination of the Hybrid Steepest-Descent Method and the Viscosity Approximation," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 911-930, March.
    13. 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.
    14. ChangAn Tian & Yisheng Song, 2013. "Strong convergence of a regularization method for Rockafellar’s proximal point algorithm," Journal of Global Optimization, Springer, vol. 55(4), pages 831-837, April.
    15. Haiyun Zhou & Peiyuan Wang, 2014. "A Simpler Explicit Iterative Algorithm for a Class of Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 716-727, June.
    16. Phayap Katchang & Poom Kumam, 2013. "An iterative algorithm for common fixed points for nonexpansive semigroups and strictly pseudo-contractive mappings with optimization problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1563-1589, August.
    17. Abkar, A. & Tavakkoli, M., 2015. "A new algorithm for two finite families of demicontractive mappings and equilibrium problems," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 491-500.
    18. Rattanaporn Wangkeeree & Narin Petrot & Rabian Wangkeeree, 2011. "The general iterative methods for nonexpansive mappings in Banach spaces," Journal of Global Optimization, Springer, vol. 51(1), pages 27-46, September.
    19. H. K. Xu & T. H. Kim, 2003. "Convergence of Hybrid Steepest-Descent Methods for Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 185-201, October.
    20. Yonghong Yao & Yeong-Cheng Liou & Shin Kang, 2010. "Minimization of equilibrium problems, variational inequality problems and fixed point problems," Journal of Global Optimization, Springer, vol. 48(4), pages 643-656, December.

    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:12:y:2024:i:18:p:2877-:d:1478821. 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.