{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,5]],"date-time":"2026-07-05T04:14:15Z","timestamp":1783224855599,"version":"3.54.6"},"reference-count":53,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"name":"Italian Minister of University and Research MUR","award":["P20229SH29"],"award-info":[{"award-number":["P20229SH29"]}]},{"name":"Italian Minister of University and Research MUR","award":["CUP: J53D23015950001"],"award-info":[{"award-number":["CUP: J53D23015950001"]}]},{"name":"Italian Minister of University and Research MUR","award":["20229FX3B9"],"award-info":[{"award-number":["20229FX3B9"]}]},{"name":"Italian Minister of University and Research MUR","award":["CUP: J53D23000660001"],"award-info":[{"award-number":["CUP: J53D23000660001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2026,4,30]]},"DOI":"10.1137\/25m1728946","type":"journal-article","created":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T08:02:15Z","timestamp":1776067335000},"page":"1831-1862","source":"Crossref","is-referenced-by-count":2,"title":["Image Resizing by Neural Network Operators and their Convergence Rate with Respect to the \\(\\boldsymbol{L}\\)\\(^{p}\\)-norm and the Dissimilarity Index Defined through the Continuous SSIM"],"prefix":"10.1137","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8834-8877","authenticated-orcid":true,"given":"Danilo","family":"Costarelli","sequence":"first","affiliation":[{"name":"Corresponding author. Department of Mathematics and Computer Science, University of Perugia, 06123 Perugia, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mariarosaria","family":"Natale","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Perugia, 06123 Perugia, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-9440-3383","authenticated-orcid":true,"given":"Michele","family":"Piconi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Perugia, 06123 Perugia, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,4,13]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1997.5494"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2011.01.003"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2021.116087"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-08801-3_5"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/0731059"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-25388-6"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2012.03.001"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2011.2173206"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.07.021"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(05)80020-6"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1080\/02664760802061970"},{"key":"ref12","first-page":"1713912","volume":"2022","author":"Chen H.","year":"2022","journal-title":"J. Funct. Spaces"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.05.001"},{"key":"ref14","first-page":"101","volume":"14","author":"Chen Z.","year":"2012","journal-title":"J. Comput. Anal. Appl."},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1007\/s00009-022-02138-8"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-024-02146-9"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2023.105944"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s00009-024-02752-8"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2013.03.015"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2013.07.009"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/BF02551274"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-021-09548-z"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02888-9"},{"key":"ref24","volume-title":"Higher-Order Derivatives and Taylor\u2019s Formula in Several Variables","author":"Folland G. B.","year":"2005"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.5201\/ipol.2011.g_lmii"},{"key":"ref26","doi-asserted-by":"crossref","unstructured":"A. Hore and D. Ziou, Image quality metrics: PSNR vs. SSIM, in Proceedings of the 20th International Conference on Pattern Recognition, IEEE, 2010, pp. 2366\u20132369.","DOI":"10.1109\/ICPR.2010.579"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2022.114426"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2022.110018"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/TASSP.1981.1163711"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2023.105941"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2018.2888517"},{"key":"ref32","doi-asserted-by":"crossref","unstructured":"C. Ledig, L. Theis, F. Husz\u00e1r, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, and Z. Wang, Photo-realistic single image super-resolution using a generative adversarial network, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2017, pp. 4681\u20134690.","DOI":"10.1109\/CVPR.2017.19"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-023-01384-6"},{"key":"ref34","doi-asserted-by":"crossref","unstructured":"B. Lim, S. Son, H. Kim, S. Nah, and K. M. Lee, Enhanced deep residual networks for single image super-resolution, in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, 2017, pp. 136\u2013144.","DOI":"10.1109\/CVPRW.2017.151"},{"key":"ref35","doi-asserted-by":"crossref","unstructured":"J. Liu, Z. Gan, and X. Zhu, Directional bicubic interpolation \u2013 A new method of image super-resolution, in Proceedings of the 3rd International Conference on Multimedia Technology, Atlantis Press, 2013, pp. 463\u2013470.","DOI":"10.2991\/icmt-13.2013.57"},{"key":"ref36","first-page":"27","volume":"14","author":"Marchetti F.","year":"2021","journal-title":"Dolomites Res. Notes Approx."},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1137\/22M147637X"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1553\/etna_vol59s295"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-022-01135-6"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-021-09542-5"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1142\/S0219530522400103"},{"key":"ref42","first-page":"136","volume":"164","author":"Popov V. A.","year":"1983","journal-title":"Tr. Mat. Inst. Steklova"},{"key":"ref43","first-page":"126781","volume":"418","author":"Qian Y.","year":"2022","journal-title":"Appl. Math. Comput."},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9045(89)90117-2"},{"key":"ref45","volume-title":"The Averaged Moduli of Smoothness: With Applications in Numerical Methods and Approximation","author":"Sendov B. K.","year":"1988"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-006-0659-y"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3991(81)90061-9"},{"key":"ref48","unstructured":"Image Processing Repository, Vision and Image Processing Lab, University of Waterloo, https:\/\/links.uwaterloo.ca\/Repository.html."},{"key":"ref49","doi-asserted-by":"crossref","unstructured":"X. Wang, K. Yu, S. Wu, J. Gu, Y. Liu, C. Dong, Y. Qiao, and C. C. Loy, ESRGAN: Enhanced super-resolution generative adversarial networks, in Proceedings of the European Conference on Computer Vision (ECCV) Workshops, 2018.","DOI":"10.1007\/978-3-030-11021-5_5"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1109\/97.995823"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2003.819861"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-021-09546-1"},{"key":"ref53","series-title":"Grad. Texts in Math. 120","volume-title":"Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation","author":"Ziemer W. P.","year":"2012"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T08:02:27Z","timestamp":1776067347000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/25M1728946"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,13]]},"references-count":53,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4,30]]}},"alternative-id":["10.1137\/25M1728946"],"URL":"https:\/\/doi.org\/10.1137\/25m1728946","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,13]]}}}