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 Semi-Iterative Method for Computing the Generalized InverseAT,S(2)

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Xiaoji Liu ◽  
Caijing Jiang
Keyword(s):  
Iterative Method ◽  
Banach Spaces ◽  
Error Bounds ◽  
Generalized Inverse

The main aim of this paper is to compute the generalized inverseAT,S(2)over Banach spaces by using semi-iterative method and to present the error bounds of the semi-iterative method for approximatingAT,S(2).

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