@MISC{NDIFF13.MIZ,
  AUTHOR = {Nakasho, Kazuhisa and Shidama, Yasunari},
  TITLE = {Higher-Order Differentiation and Inverse Function Theorem in Real Normed Spaces},
  SECTION1 = {Foundations of Differentiation in Real Normed Spaces},
  SECTION2 = {Higher-Order Differentiation and Function Composition},
  SECTION3 = {Partial Differentiation of Vector-Valued Functions},
  SECTION4 = {Higher-Order Differentiability of Inverse Function Theorem},
  DAY = {24},
  MONTH = {December},
  YEAR = {2024},
  ADDRESS1 = {Yamaguchi University\\Yamaguchi, Japan},
  ADDRESS2 = {Karuizawa Hotch 244-1\\Nagano, Japan},
  MSC2020 = {26B05 46T20 68V20},
  KEYWORDS = {higher-order derivative; inverse function theorem; real normed space; vector-valued function; },
  SUMMARY = {This article extends the theory of differentiation in real normed spaces,
  focusing on higher-order derivatives and the inverse function theorem. The work presents
  a~comprehensive treatment of higher-order derivatives for vector-valued functions and develops
  theorems on the composition of differentiable functions and their higher-order derivatives.
  It provides an analysis of partial derivatives for multivariable vector-valued functions and extends
  the inverse function theorem to higher-order differentiability, including continuity properties.
  Additionally, the article formalizes the differentiability of the inversion operator on invertible
  linear operators.
  We referred to \cite{miyadera:1972}, \cite{yoshida:1980}, \cite{Schwartz1997a}, \cite{Schwartz1997b}
   in this formalization.},
  ACKNOWLEDGEMENT = {This work was supported by JSPS KAKENHI Grant Number 24K14897.}}

