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Bounded slope variation and generalized convexity


Author: Frank N. Huggins
Journal: Proc. Amer. Math. Soc. 65 (1977), 65-69
MSC: Primary 26A45; Secondary 26A42, 26A51
DOI: https://doi.org/10.1090/S0002-9939-1977-0466447-X
MathSciNet review: 0466447
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Abstract: In this paper, the concept of bounded slope variation, that of the convexity of a function with respect to an increasing function, and the Lebesgue-Stieltjes integral are used to further generalize a theorem of F. Riesz and to give a new proof based on a weaker hypothesis that a function which has bounded slope variation with respect to an increasing function m over [a, b] can be expressed as the difference of two functions each cf which is convex with respect to m on [a, b].


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0466447-X
Keywords: Bounded slope variation, bounded variation, convex function, Lebesgue-Stieltjes integral
Article copyright: © Copyright 1977 American Mathematical Society

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