{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T20:42:50Z","timestamp":1767904970379,"version":"3.49.0"},"reference-count":17,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Higher Education Commission"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We present an efficient and simple algorithm to generate 4-point<jats:italic>n<\/jats:italic>-ary interpolating schemes. Our algorithm is based on three simple steps: second divided differences, determination of position of vertices by using second divided differences, and computation of new vertices. It is observed that 4-point<jats:italic>n<\/jats:italic>-ary interpolating schemes generated by completely different frameworks (i.e., Lagrange interpolant and wavelet theory) can also be generated by the proposed algorithm. Furthermore, we have discussed continuity, H\u00f6lder regularity, degree of polynomial generation, polynomial reproduction, and approximation order of the schemes.<\/jats:p>","DOI":"10.1155\/2013\/893414","type":"journal-article","created":{"date-parts":[[2013,11,14]],"date-time":"2013-11-14T16:16:11Z","timestamp":1384445771000},"page":"1-8","source":"Crossref","is-referenced-by-count":4,"title":["Four-Point<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>-Ary Interpolating Subdivision Schemes"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0441-8485","authenticated-orcid":true,"given":"Ghulam","family":"Mustafa","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Punjab, Bahawalpur 63100, Pakistan"}]},{"given":"Robina","family":"Bashir","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Punjab, Bahawalpur 63100, Pakistan"}]}],"member":"311","reference":[{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(86)90077-6"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01889598"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(87)90001-X"},{"issue":"1","key":"11","first-page":"434","volume":"4","year":"2009","journal-title":"Applications and Applied Mathematics"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/s00607-010-0108-x"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/205863"},{"issue":"1","key":"12","first-page":"35","volume":"2","year":"1980","journal-title":"IEEE Transaction on Pattern Analysis and Machine Intelligence"},{"issue":"6","key":"4","first-page":"183","volume":"10","year":"1978","journal-title":"Computer Aided Geometric Design"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(01)00040-1"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(03)00026-8"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2009.09.002"},{"key":"10","first-page":"199","volume-title":"Ternary and three-point univariate subdivision schemes","year":"2002"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2010.11.002"},{"key":"9","series-title":"Summer School Lecture Notes, Mathematics and Visualization","year":"2002"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492902000028"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1137\/0523086"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2013.02.001"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/893414.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/893414.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2013\/893414.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T15:21:40Z","timestamp":1469892100000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2013\/893414\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":17,"alternative-id":["893414","893414"],"URL":"https:\/\/doi.org\/10.1155\/2013\/893414","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}