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Generalized convex functions and best $ L\sb p$ approximation


Authors: Ronald M. Mathsen and Vasant A. Ubhaya
Journal: Proc. Amer. Math. Soc. 114 (1992), 733-740
MSC: Primary 26A51; Secondary 41A50
DOI: https://doi.org/10.1090/S0002-9939-1992-1088444-4
MathSciNet review: 1088444
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Abstract: Some properties of generalized convex functions significant to approximation theory are obtained. The existence of a best $ {L_p}$ approximation $ (1 \leq p \leq \infty )$ from subsets of these functions is established under certain conditions. Special cases of these functions include $ n$-convex functions which are much investigated in the literature.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1088444-4
Article copyright: © Copyright 1992 American Mathematical Society

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