This is a study of best approximation with certain geometric constraints. Two major problem areas are considered: best Lp approximation to a function in Lp (0,1) by convex functions, (m, n)-convex functions, (m, n)-convex functions and (m, n)-convex splines, for 1 < p < ∞ , and best uniform approximation to a continuous function by convex functions, quasi-convex functions and piecewise monotone functions.
","abstract_html":"<p>This is a study of best approximation with certain geometric constraints. Two major problem areas are considered: best L<sub>p</sub> approximation to a function in L<sub>p </sub>(0,1) by convex functions, (m, n)-convex functions, (m, n)-convex functions and (m, n)-convex splines, for 1 < p < ∞ , and best uniform approximation to a continuous function by convex functions, quasi-convex functions and piecewise monotone functions.</p>","abstract_has_math":false,"creators":["Xu, Yuesheng"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics & Statistics","degree_department":null,"school":null,"contributors":["S. E. Weinstein","M. Bartelt","John Swetits","Hideaki Kaneko"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":1989,"date_issued":"1989-07-01T07:00:00Z","date_published":"1989-07-01T07:00:00Z","updated_at":"2026-07-24T03:35:23Z","subjects":["Approximation theory","Geometrical constructions","Mathematics"],"languages":[],"rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
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"]},{"key":"dc:title","label":"Title","values":["Best Approximation With Geometric Constraints"]}]}],"canonical_facts":{"dc:contributor":["S. E. Weinstein","M. Bartelt","John Swetits","Hideaki Kaneko"],"dc:creator":["Xu, Yuesheng"],"dc:date.available":["2019-10-16T07:00:00Z"],"dc:description.abstract":["This is a study of best approximation with certain geometric constraints. Two major problem areas are considered: best Lp approximation to a function in Lp (0,1) by convex functions, (m, n)-convex functions, (m, n)-convex functions and (m, n)-convex splines, for 1 < p < ∞ , and best uniform approximation to a continuous function by convex functions, quasi-convex functions and piecewise monotone functions.
"],"dc:identifier":["https://digitalcommons.odu.edu/mathstat_etds/106"],"dc:rights":["In Copyright. URI: http://rightsstatements.org/vocab/InC/1.0/ This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
"],"dc:subject":["Approximation theory","Geometrical constructions","Mathematics"],"dc:title":["Best Approximation With Geometric Constraints"],"thesis:degree_discipline":["Mathematics & Statistics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T03:35:23Z"}