Mean-value theorem for vector-valued functions

Title:

Mean-value theorem for vector-valued functions

Creator:

Matkowski, Janusz

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:0a1c1ab4-1a6e-4931-9852-d427e210b728
uuid:0a1c1ab4-1a6e-4931-9852-d427e210b728
doi:10.21136/MB.2012.142997

Subject:

Lagrange mean-value theorem, mean, Darboux property of derivative, and vector-valued function

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

For a differentiable function f : I → ℝ k , where I is a real interval and k ∈ ℕ, a counterpart of the Lagrange mean-value theorem is presented. Necessary and sufficient conditions for the existence of a mean M : I 2 → I such that f (x) − f (y) = (x − y)f ′ (M(x,y)), x,y ∈ I, are given. Similar considerations for a theorem accompanying the Lagrange mean-value theorem are presented.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

415-423

Source:

Mathematica bohemica | 2012 Volume:137 | Number:4

Harvested from:

CDK

Metadata only:

false