scholarly journals Representations for the Bloch Type Semi-norm of Fréchet Differentiable Mappings

2020 ◽  
Author(s):  
Marijan Marković
Keyword(s):  
Fréchet Differentiable ◽  
Differentiable Mappings

scholarly journals Some Grüss Type Inequalities for Fréchet Differentiable Mappings

2020 ◽  
Vol 44 (4) ◽  
pp. 571-579
Author(s):  
T. TEIMOURI-AZADBAKHT ◽  
A. G GHAZANFARI
Keyword(s):  
Open Neighborhood ◽  
Continuous Functions ◽  
Inner Product ◽  
C Algebra ◽  
Inner Products ◽  
Fréchet Differentiable ◽  
Grüss Type Inequalities ◽  
Differentiable Mappings

Let X be a Hilbert C∗-module on C∗-algebra A and p ∈ A. We denote by Dp(A,X) the set of all continuous functions f : A → X, which are Fréchet differentiable on a open neighborhood U of p. Then, we introduce some generalized semi-inner products on Dp(A,X), and using them some Grüss type inequalities in semi-inner product C∗-module Dp(A,X) and Dp(A,Xn) are established.

scholarly journals On the semigroup of differentiable mappings

1969 ◽  
Vol 10 (3-4) ◽  
pp. 503-510 ◽  
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Banach Space ◽  
Real Banach Space ◽  
Fréchet Differentiable ◽  
Differentiable Mappings

The purpose of this paper is to improve a result in [2] on the automorphisms of the semigroup D = D(E) of all (Fréchet)-differentiable mappings of a real Banach space E into itself.

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 A NEW GENERALIZATION OF THE TRAPEZOID FORMULA FOR n-TIME DIFFERENTIABLE MAPPINGS AND APPLICATIONS

2000 ◽  
Vol 33 (4) ◽  
Author(s):  
P. Cerone ◽  
S. S. Dragomir ◽  
J. Roumeliotis ◽  
J. Šunde
Keyword(s):  
Differentiable Mappings
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