Article citationsMore>>

A. M. Russell and C. J. F. Upton, “A Generalization of a Theorem by F. Riesz,” Mathematical Analysis, Vol. 9, No. 1, 1983, pp. 69-77. doi:10.1007/BF01903991

has been cited by the following article:

• TITLE: On Second Riesz Φ-Variation of Normed Space Valued Maps

  AUTHORS: Mireya Bracamonte, José Giménez, N. Merentes, J. L. Sánchez

  KEYWORDS: Young Function; Φ-Variation; Second Φ-Variation of a Function

  JOURNAL NAME: Advances in Pure Mathematics, Vol.2 No.1, January 6, 2012

  ABSTRACT: In this article we present a Riesz-type generalization of the concept of second variation of normed space valued functions defined on an interval [a,b]R. We show that a function f [a,b], where X is a reflexive Banach space, is of bounded second Φ-variation, in the sense of Riesz, if and only if it can be expressed as the (Bochner) integral of a function of bounded (first) $\Phi$-variation. We provide also a Riesz lemma type inequality to estimate the total second Riesz-Φ-variation introduced.