IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v187y2021icp215-230.html
   My bibliography  Save this article

Best proximity points of (EP)-operators with qualitative analysis and simulation

Author

Listed:
  • Usurelu, Gabriela Ioana
  • Turcanu, Teodor

Abstract

In this paper, we analyze a Thakur three-step iterative process adapted for the context of non-self-mappings. Based on this iteration, we state and prove the existence of best proximity points for the recently introduced class of (EP)-non-self-mappings. Under certain assumptions, we study the convergence of the considered Thakur process to a best proximity point for the same class of operators. Moreover, we design a CQ-type algorithm which strongly converges to a best proximity point of such kind of mappings. In addition, we present the CQ-variant of the proposed algorithm that strongly converges to a best proximity pair. Some examples and numerical simulations sustain the efficiency of our new algorithms.

Suggested Citation

  • Usurelu, Gabriela Ioana & Turcanu, Teodor, 2021. "Best proximity points of (EP)-operators with qualitative analysis and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 215-230.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:215-230
    DOI: 10.1016/j.matcom.2021.02.022
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421000616
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.02.022?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. Ilchev, A. & Zlatanov, B., 2016. "Error estimates for approximation of coupled best proximity points for cyclic contractive maps," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 412-425.
    2. Yulia Dzhabarova & Stanimir Kabaivanov & Margarita Ruseva & Boyan Zlatanov, 2020. "Existence, Uniqueness and Stability of Market Equilibrium in Oligopoly Markets," Administrative Sciences, MDPI, vol. 10(3), pages 1-32, September.
    3. Thakur, Balwant Singh & Thakur, Dipti & Postolache, Mihai, 2016. "A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 147-155.
    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. Maryam Gharamah Alshehri & Faizan Ahmad Khan & Faeem Ali, 2022. "An Iterative Algorithm to Approximate Fixed Points of Non-Linear Operators with an Application," Mathematics, MDPI, vol. 10(7), pages 1-16, April.
    2. Yonghong Yao & Mihai Postolache & Jen-Chih Yao, 2019. "Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators," Mathematics, MDPI, vol. 7(12), pages 1-13, December.
    3. 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.
    4. Chanchal Garodia & Afrah A. N. Abdou & Izhar Uddin, 2021. "A New Modified Fixed-Point Iteration Process," Mathematics, MDPI, vol. 9(23), pages 1-10, December.
    5. Gdawiec, Krzysztof & Kotarski, Wiesław, 2017. "Polynomiography for the polynomial infinity norm via Kalantari’s formula and nonstandard iterations," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 17-30.
    6. Yuanheng Wang & Mingyue Yuan & Bingnan Jiang, 2021. "Multi-Step Inertial Hybrid and Shrinking Tseng’s Algorithm with Meir–Keeler Contractions for Variational Inclusion Problems," Mathematics, MDPI, vol. 9(13), pages 1-13, July.
    7. Yonghong Yao & Mihai Postolache & Jen-Chih Yao, 2019. "An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems," Mathematics, MDPI, vol. 7(1), pages 1-15, January.
    8. Laura Ajeti & Atanas Ilchev & Boyan Zlatanov, 2022. "On Coupled Best Proximity Points in Reflexive Banach Spaces," Mathematics, MDPI, vol. 10(8), pages 1-19, April.
    9. 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.
    10. Miroslav Hristov & Atanas Ilchev & Boyan Zlatanov, 2020. "On the Best Proximity Points for p –Cyclic Summing Contractions," Mathematics, MDPI, vol. 8(7), pages 1-11, July.
    11. Austine Efut Ofem & Jacob Ashiwere Abuchu & Reny George & Godwin Chidi Ugwunnadi & Ojen Kumar Narain, 2022. "Some New Results on Convergence, Weak w 2 -Stability and Data Dependence of Two Multivalued Almost Contractive Mappings in Hyperbolic Spaces," Mathematics, MDPI, vol. 10(20), pages 1-26, October.
    12. S. Kabaivanov & V. Zhelinski & B. Zlatanov, 2021. "Coupled Fixed Points for Hardy-Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions," Papers 2110.01496, arXiv.org.
    13. Javid Ali & Faeem Ali & Puneet Kumar, 2019. "Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
    14. Yulia Dzhabarova & Stanimir Kabaivanov & Margarita Ruseva & Boyan Zlatanov, 2020. "Existence, Uniqueness and Stability of Market Equilibrium in Oligopoly Markets," Administrative Sciences, MDPI, vol. 10(3), pages 1-32, September.
    15. Mujahid Abbas & Muhammad Waseem Asghar & Manuel De la Sen, 2022. "Approximation of the Solution of Delay Fractional Differential Equation Using AA -Iterative Scheme," Mathematics, MDPI, vol. 10(2), pages 1-20, January.
    16. Konrawut Khammahawong & Parin Chaipunya & Kamonrat Sombut, 2022. "Approximating Common Fixed Points of Nonexpansive Mappings on Hadamard Manifolds with Applications," Mathematics, MDPI, vol. 10(21), pages 1-20, November.
    17. Ali Abkar & Mohsen Shekarbaigi, 2017. "A Novel Iterative Algorithm Applied to Totally Asymptotically Nonexpansive Mappings in CAT(0) Spaces," Mathematics, MDPI, vol. 5(1), pages 1-13, February.
    18. Wissam Kassab & Teodor Ţurcanu, 2019. "Numerical Reckoning Fixed Points of ( ρE )-Type Mappings in Modular Vector Spaces," Mathematics, MDPI, vol. 7(5), pages 1-13, April.

    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:187:y:2021:i:c:p:215-230. 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.