IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v164y2022ics0960077922006592.html
   My bibliography  Save this article

Interpolative operators: Fractal to multivalued fractal

Author

Listed:
  • Prithvi, B.V.
  • Katiyar, S.K.

Abstract

The present endeavor investigates an area concerning interpolative operators to approach attractors, particularly fractals; ergo, an interpolative iterated operator system (Iδ-IOS) is employed. As a consequence, dull and active fractals are perceived for the first time in the literature. Moreover, fractal function thereby fractal interpolation space is ascertained using an introductory e-metric and a finite collection of modified Berinde weak operators. Further, the investigation is extended onto multivalued fractals via set-valued interpolative operators. Cut to, properties of a multi-operator associated with set-valued IOS are explored.

Suggested Citation

  • Prithvi, B.V. & Katiyar, S.K., 2022. "Interpolative operators: Fractal to multivalued fractal," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922006592
    DOI: 10.1016/j.chaos.2022.112449
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922006592
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112449?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. Erdal Karapinar & Ravi Agarwal & Hassen Aydi, 2018. "Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces," Mathematics, MDPI, vol. 6(11), pages 1-7, November.
    2. Chifu, Cristian & Petruşel, Adrian, 2008. "Multivalued fractals and generalized multivalued contractions," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 203-210.
    3. Llorens-Fuster, Enrique & Petruşel, Adrian & Yao, Jen-Chih, 2009. "Iterated function systems and well-posedness," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1561-1568.
    4. Singh, S.L. & Prasad, Bhagwati & Kumar, Ashish, 2009. "Fractals via iterated functions and multifunctions," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1224-1231.
    5. Andres, Jan & Fišer, Jiří & Gabor, Grzegorz & Leśniak, Krzysztof, 2005. "Multivalued fractals," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 665-700.
    6. Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2008. "From iterated function systems to iterated multifunction systems," Departmental Working Papers 2008-39, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    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. Ullah, Kifayat & Katiyar, S.K., 2023. "Generalized G-Hausdorff space and applications in fractals," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Agathiyan, A. & Gowrisankar, A. & Fataf, Nur Aisyah Abdul, 2024. "On the integral transform of fractal interpolation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 209-224.
    3. Prithvi, B.V. & Katiyar, S.K., 2023. "Revisiting fractal through nonconventional iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

    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. Prithvi, B.V. & Katiyar, S.K., 2023. "Revisiting fractal through nonconventional iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Andres, Jan & Rypka, Miroslav, 2013. "Dimension of hyperfractals," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 146-154.
    3. Ullah, Kifayat & Katiyar, S.K., 2023. "Generalized G-Hausdorff space and applications in fractals," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Llorens-Fuster, Enrique & Petruşel, Adrian & Yao, Jen-Chih, 2009. "Iterated function systems and well-posedness," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1561-1568.
    5. Thangaraj, C. & Easwaramoorthy, D. & Selmi, Bilel & Chamola, Bhagwati Prasad, 2024. "Generation of fractals via iterated function system of Kannan contractions in controlled metric space," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 188-198.
    6. Bucci, Alberto & Florio, Massimo & La Torre, Davide, 2012. "Government spending and growth in second-best economies," Economic Modelling, Elsevier, vol. 29(3), pages 654-663.
    7. Abbas, Mujahid & Anjum, Rizwan & Iqbal, Hira, 2022. "Generalized enriched cyclic contractions with application to generalized iterated function system," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    8. Erdal Karapınar & Ravi P. Agarwal & Seher Sultan Yeşilkaya & Chao Wang, 2022. "Fixed-Point Results for Meir–Keeler Type Contractions in Partial Metric Spaces: A Survey," Mathematics, MDPI, vol. 10(17), pages 1-76, August.
    9. Altun, Ishak & Sahin, Hakan & Aslantas, Mustafa, 2021. "A new approach to fractals via best proximity point," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Vincenzo CAPASSO & Herb E. KUNZE & Davide LA TORRE & Edward R. VRSCAY, 2008. "Parameter identification for deterministic and stochastic differential equations using the "collage method" for fixed point equations," Departmental Working Papers 2008-08, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    11. Saleem, Naeem & Ahmad, Khaleel & Ishtiaq, Umar & De la Sen, Manuel, 2023. "Multivalued neutrosophic fractals and Hutchinson-Barnsley operator in neutrosophic metric space," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    12. Petruşel, Adrian & Petruşel, Gabriela, 2019. "Coupled fractal dynamics via Meir–Keeler operators," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 206-212.
    13. Reny George & Hemanth Kumar Pathak, 2020. "Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications," Mathematics, MDPI, vol. 9(1), pages 1-21, December.
    14. La Torre, Davide & Marsiglio, Simone & Mendivil, Franklin & Privileggi, Fabio, 2015. "Self-similar measures in multi-sector endogenous growth models," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 40-56.
    15. Zhang, Yongping & Sun, Weihua & Liu, Shutang, 2009. "Control of generalized Julia sets," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1738-1744.
    16. Singh, S.L. & Prasad, Bhagwati & Kumar, Ashish, 2009. "Fractals via iterated functions and multifunctions," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1224-1231.
    17. Miculescu, Radu & Mihail, Alexandru & Urziceanu, Silviu-Aurelian, 2020. "Contractive affine generalized iterated function systems which are topologically contracting," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    18. Davide LA TORRE & Edward R. VRSCAY, 2008. "A generalized fractal transform for measure-valued images," Departmental Working Papers 2008-38, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    19. Chifu, Cristian & Petruşel, Adrian, 2008. "Multivalued fractals and generalized multivalued contractions," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 203-210.
    20. Jaroszewska, Joanna, 2013. "A note on iterated function systems with discontinuous probabilities," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 28-31.

    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:chsofr:v:164:y:2022:i:c:s0960077922006592. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.