A duality approach to best uniform convex approximation (Q1192528)

Let C[a,b] be the space of continuous functions on [a,b] endowed with the uniform norm.Let K be the set of convex functions defined on [a,b].In this paper a duality theorem that expresses the error of the best approximation by means of the elements of K in terms of the supremum of a linear functional is established and this duality to obtain the bounds for the error of best approximation is also used. A similar duality approach has been used by \textit{V. A. Ubhaya} [J. Approximation Theory 12, 146-159 (1974; Zbl 0288.41019)]\ and by the author [J. Math. Anal. Appl. 152, No. 1, 240-251 (1990; Zbl 0729.41026)] to investigate best monotone approximation and best quasi-convex approximation,respectively.