Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 0466447
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A45, 26A42, 26A51

Retrieve articles in all journals with MSC: 26A45, 26A42, 26A51


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0466447-X
PII: S 0002-9939(1977)0466447-X
Keywords: Bounded slope variation, bounded variation, convex function, Lebesgue-Stieltjes integral
Article copyright: © Copyright 1977 American Mathematical Society