Search results for "Rolle's Theorem"

Rolle's Theorem Fails in l2

1996

MR3136895 Reviewed Ray, S.; Garai, A. The Laplace derivative. Math. Student 81 (2012), no. 1-4, 171–175. (Reviewer: Pasquale Vetro) 26A24

2014

In this paper the authors consider the Laplace derivative of a real function of a real variable introduced by R. E. Svetic [Comment. Math. Univ. Carolin. 42 (2001), no. 2, 331–343; MR1832151 (2002d:26008)]. The aim of this paper is to study the properties of the first-order Laplace derivative. They also prove Rolle's theorem, Darboux's theorem and other such theorems for the Laplace derivative.

Rolle's Theorem for Polynomials of Degree Four in a Hilbert Space

2002

AbstractIn an infinite-dimensional real Hilbert space, we introduce a class of fourth-degree polynomials which do not satisfy Rolle's Theorem in the unit ball. Extending what happens in the finite-dimensional case, we show that every fourth-degree polynomial defined by a compact operator satisfies Rolle's Theorem.

An approximate Rolle's theorem for polynomials of degree four in a Hilbert space

2005

We show that the fourth degree polynomials that satisfy Rolle’s Theorem in the unit ball of a real Hilbert space are dense in the space of polynomials that vanish in the unit sphere. As a consequence, we obtain a sort of approximate Rolle’s Theorem for those polynomials.