scholarly journals Mean-value theorem for vector-valued functions

2012 ◽  
Vol 137 (4) ◽  
pp. 415-423 ◽  
Author(s):  
Janusz Matkowski
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Vector Valued Functions ◽  
Vector Valued

scholarly journals On some mean value theorems of the differential calculus

1971 ◽  
Vol 5 (2) ◽  
pp. 227-238 ◽  
Author(s):  
J.B. Diaz ◽  
R. Výborný
Keyword(s):  
Differential Calculus ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Mean Value Theorems ◽  
Partial Converse ◽  
Generalized Mean ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Special Case

A general mean value theorem, for real valued functions, is proved. This mean value theorem contains, as a special case, the result that for any, suitably restricted, function f defined on [a, b], there always exists a number c in (a, b) such that f(c) − f(a) = f′(c)(c−a). A partial converse of the general mean value theorem is given. A similar generalized mean value theorem, for vector valued functions, is also established.

The Mean Value Theorem for Vector Valued Functions: A Simple Proof

1979 ◽  
Vol 52 (3) ◽  
pp. 157 ◽  
Author(s):  
William S. Hall ◽  
Martin L. Newell
Keyword(s):  
Simple Proof ◽  
Mean Value ◽  
Mean Value Theorem ◽  
The Mean ◽  
Vector Valued Functions ◽  
Vector Valued

scholarly journals Mean Value Theorems for Vector Valued Functions

1965 ◽  
Vol 14 (3) ◽  
pp. 197-209 ◽  
Author(s):  
Robert M. McLeod
Keyword(s):  
Differential Calculus ◽  
Closed Interval ◽  
Open Interval ◽  
Mean Value ◽  
Mean Value Theorem ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Image Position ◽  
Vector Valued Functions ◽  
Vector Valued

The object of this paper is to give a generalisation to vector valued functions of the classical mean value theorem of differential calculus. In that theorem we havefor some c in the open interval a, b when f is a real valued function which is continuous on the closed interval a, b and differentiable on the open interval. The counterpart to (1) when f has values in an n-dimensional vector space turns out to bewhere cka, b, 0 k, and .

scholarly journals Mean value theorems and a Taylor theorem for vector valued functions

1981 ◽  
Vol 24 (1) ◽  
pp. 69-77
Author(s):  
Rudolf Výborný
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Extension Theorem ◽  
Mean Value ◽  
Mean Value Theorems ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Convex

Two mean value theorems and a Taylor theorem for functions with values in a locally convex topological vector space are proved without the use of the Hahn-Banach extension theorem.

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