Contracting Mapping on Normed Linear Space

Keiichi Miyajima; Artur Korniłowicz; Yasunari Shidama

The search session has expired. Please query the service again.

Displaying similar documents to “Contracting Mapping on Normed Linear Space”

Differentiable Functions on Normed Linear Spaces

Yasunari Shidama (2012)

Formalized Mathematics

Similarity:

In this article, we formalize differentiability of functions on normed linear spaces. Partial derivative, mean value theorem for vector-valued functions, continuous differentiability, etc. are formalized. As it is well known, there is no exact analog of the mean value theorem for vector-valued functions. However a certain type of generalization of the mean value theorem for vector-valued functions is obtained as follows: If ||ƒ'(x + t · h)|| is bounded for t between 0 and 1 by some constant...

A note on the paper “Characterizations on 2-isometries”.

Abbassi, Hossein, Nourouzi, Kourosh (2009)

International Journal of Open Problems in Computer Science and Mathematics. IJOPCM

Similarity:

Differentiation in Normed Spaces

Noboru Endou, Yasunari Shidama (2013)

Formalized Mathematics

Similarity:

In this article we formalized the Fréchet differentiation. It is defined as a generalization of the differentiation of a real-valued function of a single real variable to more general functions whose domain and range are subsets of normed spaces [14].

$2$ -nsr lemma and quotient space in $2$ -normed space

P. Riyas, K. T. Ravindran (2011)

Matematički Vesnik

Similarity:

Isometric Differentiable Functions on Real Normed Space

Yuichi Futa, Noboru Endou, Yasunari Shidama (2013)

Formalized Mathematics

Similarity:

In this article, we formalize isometric differentiable functions on real normed space [17], and their properties.

Riemann Integral of Functions from ℝ into Real Banach Space

Keiko Narita, Noboru Endou, Yasunari Shidama (2013)

Formalized Mathematics

Similarity:

In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements of a real normed space and finite sequences of real numbers. In addition we proved some theorems...