scholarly journals Differentiable functions on certain Banach spaces

1965 ◽  
Vol 71 (2) ◽  
pp. 393-396 ◽  
Author(s):  
Robert Bonic ◽  
John Frampton
Keyword(s):  
Banach Spaces ◽  
Differentiable Functions

scholarly journals General Norm Inequalities of Trapezoid Type for Fréchet Differentiable Functions in Banach Spaces

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1288
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Banach Spaces ◽  
Error Bounds ◽  
Norm Inequalities ◽  
Differentiable Functions ◽  
Fréchet Differentiable ◽  
General Norm

In this paper we establish some error bounds in approximating the integral by general trapezoid type rules for Fréchet differentiable functions with values in Banach spaces.

scholarly journals On the semigroup of differentiable mappings (II)

1972 ◽  
Vol 13 (2) ◽  
pp. 122-128
Author(s):  
G. R. Wood ◽  
Sadayuki Yamamuro
Keyword(s):  
Banach Spaces ◽  
Real Variable ◽  
Differentiable Functions ◽  
Finite Dimensional ◽  
Differentiable Mappings

In [2], K. D. Magill, Jr. has proved that every automorphism of the semigroup (with respect to composition) of all real-valued differentiable functions of a real variable is inner. The purpose of this paper is to generalize this fact to arbitrary finite-dimensional real Banach spaces.

scholarly journals An example on composite differentiable functions in infinite dimensions

1989 ◽  
Vol 40 (1) ◽  
pp. 91-95 ◽  
Author(s):  
J.A. Jaramillo
Keyword(s):  
Banach Spaces ◽  
Classical Result ◽  
Infinite Dimensions ◽  
Differentiable Functions ◽  
Infinitely Differentiable Functions

We present an example showing that a classical result due to Glaeser about the closedness of composition subalgebras of infinitely differentiable functions cannot be extended to the case of weakiy uniformly differentiable functions on Banach spaces.

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