{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T22:01:32Z","timestamp":1781733692164,"version":"3.54.5"},"reference-count":45,"publisher":"American Institute of Mathematical Sciences (AIMS)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MFC"],"published-print":{"date-parts":[[2025]]},"DOI":"10.3934\/mfc.2025002","type":"journal-article","created":{"date-parts":[[2025,1,17]],"date-time":"2025-01-17T05:29:24Z","timestamp":1737091764000},"page":"1059-1074","source":"Crossref","is-referenced-by-count":6,"title":["Sz&lt;inline-formula&gt;&lt;tex-math id=\"M1\"&gt;$ \\acute{a} $&lt;\/tex-math&gt;&lt;\/inline-formula&gt;sz Chlodowsky type operators coupling adjoint Bernoulli's polynomials"],"prefix":"10.3934","volume":"8","author":[{"given":"Nadeem","family":"Rao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Avinash Kumar","family":"Yadav","sequence":"additional","affiliation":[{"name":"Department of Applied Science, Galgotias College of Engg and Technology, Greater Noida, Gautam Buddha Nagar-201310, U.P., India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mohammad","family":"Shahzad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Chandigarh University, Mohali-140413, Punjab, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mamta","family":"Rani","sequence":"additional","affiliation":[{"name":"World College of Technology and Management, WCTM Campus, Farukh Nagar, Gurgaon, Delhi-NCR"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mfc.2025002-1"},{"key":"key-10.3934\/mfc.2025002-2"},{"key":"key-10.3934\/mfc.2025002-3","doi-asserted-by":"publisher","DOI":"10.36045\/bbms\/1579402817"},{"key":"key-10.3934\/mfc.2025002-4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2020.124307"},{"key":"key-10.3934\/mfc.2025002-5","doi-asserted-by":"crossref","unstructured":"<p>F. Altomare and M. Campiti, Korovkin-type approximation theory and its applications, <i>De Gruyter Ser Stud in Math.<\/i>, <b>17<\/b> (1994), 266\u2013274.<\/p>","DOI":"10.1515\/9783110884586"},{"key":"key-10.3934\/mfc.2025002-6","doi-asserted-by":"crossref","unstructured":"<p>P. Appell, Sur une class de polyn\u00f4mes, <i>Ann. Sci \u00c9c. Norm Sup\u00e9r; Soci\u00e9t\u00e9 mathe\u00e9matique de France, Paris, France<\/i>, <b>9<\/b> (1880), 119-144.<\/p>","DOI":"10.24033\/asens.186"},{"key":"key-10.3934\/mfc.2025002-7","doi-asserted-by":"publisher","DOI":"10.2298\/FIL1302371A"},{"key":"key-10.3934\/mfc.2025002-8","doi-asserted-by":"publisher","DOI":"10.1016\/j.kjs.2023.12.007"},{"key":"key-10.3934\/mfc.2025002-9","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-024-02752-0"},{"key":"key-10.3934\/mfc.2025002-10","doi-asserted-by":"publisher","DOI":"10.3934\/math.2024217"},{"key":"key-10.3934\/mfc.2025002-11","doi-asserted-by":"crossref","unstructured":"<p>M. Ayman-Mursaleen, N. Rao, M. Rani, A. Kilicman, A. A. H. A. Al-Abied and Pradeep Malik, A note on approximation of blending type bernstein\u2013schurer\u2013kantorovich operators with shape parameter $\\alpha$, <i>Journal of Mathematics<\/i>, <b>2023<\/b> (2019), Article ID 5245806, 13 pages.<\/p>","DOI":"10.1155\/2023\/5245806"},{"key":"key-10.3934\/mfc.2025002-12","unstructured":"<p>S. N. Bernstein, D$\\acute{e} $monstration du th$\\acute{e}$or$\\grave{e}$me de Weierstrass fond$\\acute{e}$e sur le calcul de probabilit$\\acute{e}$s, <i>Commun. Soc. Math. Kharkow.<\/i>, <b>13<\/b> (1913), 1\u20132.<\/p>"},{"key":"key-10.3934\/mfc.2025002-13","doi-asserted-by":"publisher","DOI":"10.1002\/mma.8134"},{"key":"key-10.3934\/mfc.2025002-14","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2024.07.015"},{"key":"key-10.3934\/mfc.2025002-15","doi-asserted-by":"crossref","unstructured":"<p>N. \u00c7etin, Approximation and geometric properties of complex $\\alpha$ -Bernstein operator, <i>Results Math<\/i>, <b>74<\/b> (2019), Article number: 40.<\/p>","DOI":"10.1007\/s00025-018-0953-z"},{"key":"key-10.3934\/mfc.2025002-16","doi-asserted-by":"publisher","DOI":"10.3906\/mat-1903-109"},{"key":"key-10.3934\/mfc.2025002-17","doi-asserted-by":"crossref","unstructured":"<p>R. A. Devore and G. G. Lorentz, <i>Constructive Approximation<\/i>, Berl\u0131n: Springer, 1993.<\/p>","DOI":"10.1007\/978-3-662-02888-9"},{"key":"key-10.3934\/mfc.2025002-18","doi-asserted-by":"crossref","unstructured":"<p>S.-Y. Huang, Y.-L. Feng and Q. Wu, Learning theory of minimum error entropy under weak moment conditions, <i>Anal. Appl.<\/i>, <b>20<\/b> (2022), 121\u2013139.<\/p>","DOI":"10.1142\/S0219530521500044"},{"key":"key-10.3934\/mfc.2025002-19","doi-asserted-by":"publisher","DOI":"10.1016\/j.bspc.2020.102343"},{"key":"key-10.3934\/mfc.2025002-20","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/6637893"},{"key":"key-10.3934\/mfc.2025002-21","doi-asserted-by":"crossref","unstructured":"<p>K. Khan and D. K. Lobiyal, B&#232;zier curves based on Lup<img src=\"mfc-2577-8838_2025002-M1.jpg\">s $(p, q)$-analogue of Bernstein functions in CAGD, <i>Comput. Appl. Math.<\/i>, <b>317<\/b> (2017), 458\u2013477.<\/p>","DOI":"10.1016\/j.cam.2016.12.016"},{"key":"key-10.3934\/mfc.2025002-22"},{"key":"key-10.3934\/mfc.2025002-23","doi-asserted-by":"publisher","DOI":"10.1016\/1385-7258(88)90007-8"},{"key":"key-10.3934\/mfc.2025002-24","doi-asserted-by":"crossref","unstructured":"<p>T. Mao, Z.-J. Shi and D.-X. Zhou, Approximating functions with multi-features by deep convolutional neural networks, <i>Analysis and Applications<\/i>, <b>21<\/b> (2023), 93\u2013125.<\/p>","DOI":"10.1142\/S0219530522400085"},{"key":"key-10.3934\/mfc.2025002-25","doi-asserted-by":"publisher","DOI":"10.1002\/mma.4559"},{"key":"key-10.3934\/mfc.2025002-26","doi-asserted-by":"publisher","DOI":"10.1007\/s40995-020-01024-w"},{"key":"key-10.3934\/mfc.2025002-27","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-019-00752-4"},{"key":"key-10.3934\/mfc.2025002-28","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.11.044"},{"key":"key-10.3934\/mfc.2025002-29","doi-asserted-by":"publisher","DOI":"10.1007\/s40995-020-01018-8"},{"key":"key-10.3934\/mfc.2025002-30","unstructured":"<p>P. Natalini and E. Ricci, Adjoint Appell\u2013Euler and first kind Appell\u2013Bernoulli's polynomials, <i>Appl.Appl. Math.<\/i>, <b>14<\/b> (2019), 1112\u20131122.<\/p>"},{"key":"key-10.3934\/mfc.2025002-31","doi-asserted-by":"publisher","DOI":"10.2298\/FIL1301173O"},{"key":"key-10.3934\/mfc.2025002-32"},{"key":"key-10.3934\/mfc.2025002-33"},{"key":"key-10.3934\/mfc.2025002-34","unstructured":"<p>R. Pratap, The Family of $\\lambda$-Bernstein-Durrmeyer operators based on certain parameters, <i>Mathematical Foundations of Computing<\/i>, <b>5<\/b> (2022), 1\u201312.<\/p>"},{"key":"key-10.3934\/mfc.2025002-35","doi-asserted-by":"crossref","unstructured":"<p>Y.-Y. Qian and D.-S. Yu, Neural network interpolation operators activated by smooth ramp functions, <i>Analysis and Applications<\/i>, <b>20<\/b> (2022), 791\u2013813.<\/p>","DOI":"10.1142\/S0219530521500123"},{"key":"key-10.3934\/mfc.2025002-36","doi-asserted-by":"publisher","DOI":"10.3390\/sym16121703"},{"key":"key-10.3934\/mfc.2025002-37"},{"key":"key-10.3934\/mfc.2025002-38","doi-asserted-by":"crossref","unstructured":"<p>N. Rao, P. Malik and M. Rani, Blending type Approximations by Kantorovich variant of $\\alpha$-Baskakov operator, <i>Palestine Journal of Mathematics<\/i>, <b>11<\/b> (2022), 402\u2013413.<\/p>","DOI":"10.22541\/au.162526026.60514857\/v1"},{"key":"key-10.3934\/mfc.2025002-39","unstructured":"<p>F. Stancu, Approximarca func\u1e6diilor de dou$\\breve{a}$ \u015fi mai multe vsrabile prin \u1e63iruri de operatori liniari \u1e63i positivi, <i>PhD Thesis, Cluj-Napoca<\/i>, 1984 (Romanian).<\/p>"},{"key":"key-10.3934\/mfc.2025002-40","doi-asserted-by":"publisher","DOI":"10.1186\/s13660-024-03199-x"},{"key":"key-10.3934\/mfc.2025002-41"},{"key":"key-10.3934\/mfc.2025002-42","doi-asserted-by":"publisher","DOI":"10.3934\/mfc.2022008"},{"key":"key-10.3934\/mfc.2025002-43","unstructured":"<p>K. Weierstrass, \u00dcber die analytische Darstellbarkeit sogenannter willk\u00fcrlicher Functionen einer reellen Ver\u00e4nderlichen, <i>Sitzungsberichte der K\u00f6niglich Preu\u00dfischen Akademie der Wissenschaften zu Berlin<\/i>, <b>2<\/b> (1885), 633-639.<\/p>"},{"key":"key-10.3934\/mfc.2025002-44"},{"key":"key-10.3934\/mfc.2025002-45","doi-asserted-by":"crossref","unstructured":"<p>Q. Zhang, M. Mu and X. Wang, A Modified robotic manipulator controller based on bernstein-kantorovich-stancu operator, <i>Micromachines<\/i>, <b>14<\/b> (2022).<\/p>","DOI":"10.3390\/mi14010044"}],"container-title":["Mathematical Foundations of Computing"],"original-title":[],"deposited":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T10:02:12Z","timestamp":1756807332000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.aimsciences.org\/\/article\/doi\/10.3934\/mfc.2025002"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":45,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2025]]}},"URL":"https:\/\/doi.org\/10.3934\/mfc.2025002","relation":{},"ISSN":["2577-8838"],"issn-type":[{"value":"2577-8838","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]}}}