{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T18:20:02Z","timestamp":1773080402498,"version":"3.50.1"},"reference-count":16,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,12,19]],"date-time":"2011-12-19T00:00:00Z","timestamp":1324252800000},"content-version":"vor","delay-in-days":352,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100004681","name":"Higher Education Commission, Pakistan","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004681","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2011,1]]},"abstract":"<jats:p>We present an explicit formula which unifies the mask of (2<jats:italic>n<\/jats:italic> \u2212 1)\u2010point ternary interpolating as well as approximating subdivision schemes. We observe that the odd point ternary interpolating and approximating schemes introduced by Lian (2009), Siddiqi and Rehan (2010, 2009) and Hassan and Dodgson (2003) are special cases of our proposed masks\/schemes. Moreover, schemes introduced by Zheng et al. (2009) can easily be generated by our proposed masks. It is also proved from comparison that (2<jats:italic>n<\/jats:italic> \u2212 1)\u2010point schemes are better than 2<jats:italic>n<\/jats:italic>\u2010scheme in the sense of computational cost, support and error bounds.<\/jats:p>","DOI":"10.1155\/2011\/832630","type":"journal-article","created":{"date-parts":[[2011,12,19]],"date-time":"2011-12-19T21:01:11Z","timestamp":1324328471000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["(2<i>n<\/i> \u2212 1)\u2010Point Ternary Approximating and Interpolating Subdivision Schemes"],"prefix":"10.1155","volume":"2011","author":[{"given":"Muhammad","family":"Aslam","sequence":"first","affiliation":[]},{"given":"Ghulam","family":"Mustafa","sequence":"additional","affiliation":[]},{"given":"Abdul","family":"Ghaffar","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,12,19]]},"reference":[{"key":"e_1_2_5_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2007.02.001"},{"key":"e_1_2_5_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01889598"},{"key":"e_1_2_5_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0167\u20108396(01)00084\u2010X"},{"key":"e_1_2_5_4_2","first-page":"199","volume-title":"Curve and Surface Fitting: Saint-Malo, 2002","author":"Hassan M. 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Constructing (2n\u2212 1)-point ternary interpolatory subdivision schemes by using variation of constants Proceedings of the International Conference on Computational Intelligence and Software Engineering (CiSE \u203209) 2009 Wuhan China https:\/\/doi.org\/10.1109\/CISE.2009.5364446.","DOI":"10.1109\/CISE.2009.5364446"},{"key":"e_1_2_5_10_2","doi-asserted-by":"crossref","unstructured":"ZhengH. HuM. andPengG. Ternary even symmetric 2n-point subdivision Proceedings of the International Conference on Computational Intelligence and Software Engineering (CiSE \u203209) 2009 Wuhan China https:\/\/doi.org\/10.1109\/CISE.2009.5363033.","DOI":"10.1109\/CISE.2009.5363033"},{"key":"e_1_2_5_11_2","doi-asserted-by":"publisher","DOI":"10.1155\/2009\/301967"},{"key":"e_1_2_5_12_2","first-page":"176","article-title":"On \u03b1-ary subdivision for curve design. 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