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Best Approximation With Geometric Constraints, Yuesheng Xu

Mathematics & Statistics Theses & Dissertations

This is a study of best approximation with certain geometric constraints. Two major problem areas are considered: best L_p approximation to a function in L_p (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.