IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v355y2019icp173-183.html
   My bibliography  Save this article

The max-product generalized sampling operators: convergence and quantitative estimates

Author

Listed:
  • Coroianu, Lucian
  • Costarelli, Danilo
  • Gal, Sorin G.
  • Vinti, Gianluca

Abstract

In this paper we study the max-product version of the generalized sampling operators based upon a general kernel function. In particular, we prove pointwise and uniform convergence for the above operators, together with a certain quantitative Jackson-type estimate based on the first order modulus of continuity of the function being approximated. The proof of the proposed results are based on the definition of the so-called generalized absolute moments. By the proposed approach, the achieved approximation results can be applied for several type of kernels, not necessarily duration-limited, such as the sinc-function, the Fejér kernel and many others. Examples of kernels with compact support for which the above theory holds can be given, for example, by the well-known central B-splines.

Suggested Citation

  • Coroianu, Lucian & Costarelli, Danilo & Gal, Sorin G. & Vinti, Gianluca, 2019. "The max-product generalized sampling operators: convergence and quantitative estimates," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 173-183.
    • Handle: RePEc:eee:apmaco:v:355:y:2019:i:c:p:173-183
    DOI: 10.1016/j.amc.2019.02.076
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319301869
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.02.076?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. Xing, Yan & Xu, Ren-zheng & Tan, Jie-qing & Fan, Wen & Hong, Ling, 2015. "A class of generalized B-spline quaternion curves," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 288-300.
    2. Mehdi Rezaeian Zadeh & Seifollah Amin & Davar Khalili & Vijay Singh, 2010. "Daily Outflow Prediction by Multi Layer Perceptron with Logistic Sigmoid and Tangent Sigmoid Activation Functions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(11), pages 2673-2688, September.
    3. Asdrubali, Francesco & Baldinelli, Giorgio & Bianchi, Francesco & Costarelli, Danilo & Rotili, Antonella & Seracini, Marco & Vinti, Gianluca, 2018. "Detection of thermal bridges from thermographic images by means of image processing approximation algorithms," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 160-171.
    4. Danilo Costarelli & Gianluca Vinti, 2017. "Convergence for a family of neural network operators in Orlicz spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 290(2-3), pages 226-235, February.
    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. Gökçer, Türkan Yeliz & Aslan, İsmail, 2022. "Approximation by Kantorovich-type max-min operators and its applications," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    2. Costarelli, Danilo & Seracini, Marco & Vinti, Gianluca, 2020. "A comparison between the sampling Kantorovich algorithm for digital image processing with some interpolation and quasi-interpolation methods," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    3. Kadak, Ugur, 2022. "Max-product type multivariate sampling operators and applications to image processing," Chaos, Solitons & Fractals, Elsevier, vol. 157(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. Tiziana Basiricò & Antonio Cottone & Daniele Enea, 2020. "Analytical Mathematical Modeling of the Thermal Bridge between Reinforced Concrete Wall and Inter-Floor Slab," Sustainability, MDPI, vol. 12(23), pages 1-21, November.
    2. David Bienvenido-Huertas & Juan Antonio Fernández Quiñones & Juan Moyano & Carlos E. Rodríguez-Jiménez, 2018. "Patents Analysis of Thermal Bridges in Slab Fronts and Their Effect on Energy Demand," Energies, MDPI, vol. 11(9), pages 1-18, August.
    3. Asdrubali, Francesco & Baldinelli, Giorgio & Bianchi, Francesco & Costarelli, Danilo & Rotili, Antonella & Seracini, Marco & Vinti, Gianluca, 2018. "Detection of thermal bridges from thermographic images by means of image processing approximation algorithms," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 160-171.
    4. Ayoub Zeroual & Mohamed Meddi & Ali A. Assani, 2016. "Artificial Neural Network Rainfall-Discharge Model Assessment Under Rating Curve Uncertainty and Monthly Discharge Volume Predictions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(9), pages 3191-3205, July.
    5. Hirad Abghari & Hojjat Ahmadi & Sina Besharat & Vahid Rezaverdinejad, 2012. "Prediction of Daily Pan Evaporation using Wavelet Neural Networks," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(12), pages 3639-3652, September.
    6. Costarelli, Danilo & Seracini, Marco & Vinti, Gianluca, 2020. "A comparison between the sampling Kantorovich algorithm for digital image processing with some interpolation and quasi-interpolation methods," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    7. Mursaleen, M. & Naaz, Ambreen & Khan, Asif, 2019. "Improved approximation and error estimations by King type (p, q)-Szász-Mirakjan Kantorovich operators," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 175-185.
    8. Mohammad Dorofki & Ahmed Elshafie & Othman Jaafar & Othman Karim & Sharifah Abdullah, 2014. "A GIS-ANN-Based Approach for Enhancing the Effect of Slope in the Modified Green-Ampt Model," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(2), pages 391-406, January.
    9. Jian Tang & Xin-An Yin & Pan Yang & ZhiFeng Yang, 2014. "Assessment of Contributions of Climatic Variation and Human Activities to Streamflow Changes in the Lancang River, China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(10), pages 2953-2966, August.
    10. Mustafa Turan & Mehmet Yurdusev, 2014. "Predicting Monthly River Flows by Genetic Fuzzy Systems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(13), pages 4685-4697, October.
    11. Ling-Xiong Han & Feng Qi, 2018. "On Approximation by Linear Combinations of Modified Summation Operators of Integral Type in Orlicz Spaces," Mathematics, MDPI, vol. 7(1), pages 1-10, December.
    12. Seyed Akrami & Vahid Nourani & S. Hakim, 2014. "Development of Nonlinear Model Based on Wavelet-ANFIS for Rainfall Forecasting at Klang Gates Dam," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(10), pages 2999-3018, August.
    13. Mohammad R. Hassanvand & Hojat Karami & Sayed-Farhad Mousavi, 2018. "Investigation of neural network and fuzzy inference neural network and their optimization using meta-algorithms in river flood routing," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 94(3), pages 1057-1080, December.
    14. Andres Ticlavilca & Mac McKee, 2011. "Multivariate Bayesian Regression Approach to Forecast Releases from a System of Multiple Reservoirs," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 25(2), pages 523-543, January.
    15. Çağlayan-Akay, Ebru & Topal, Kadriye Hilal, 2024. "Forecasting Turkish electricity consumption: A critical analysis of single and hybrid models," Energy, Elsevier, vol. 305(C).
    16. Xuesong Zhang & Kaiguang Zhao, 2012. "Bayesian Neural Networks for Uncertainty Analysis of Hydrologic Modeling: A Comparison of Two Schemes," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(8), pages 2365-2382, June.
    17. Bonakdari, Hossein & Khozani, Zohreh Sheikh & Zaji, Amir Hossein & Asadpour, Navid, 2018. "Evaluating the apparent shear stress in prismatic compound channels using the Genetic Algorithm based on Multi-Layer Perceptron: A comparative study," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 400-411.
    18. Sinan Jasim Hadi & Mustafa Tombul, 2018. "Forecasting Daily Streamflow for Basins with Different Physical Characteristics through Data-Driven Methods," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(10), pages 3405-3422, August.
    19. Costarelli, D. & Krivoshein, A. & Skopina, M. & Vinti, G., 2019. "Quasi-projection operators with applications to differential-difference expansions," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    20. Dhamija, Minakshi & Pratap, Ram & Deo, Naokant, 2018. "Approximation by Kantorovich form of modified Szász–Mirakyan operators," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 109-120.

    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:apmaco:v:355:y:2019:i:c:p:173-183. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.