Contracting Mapping on Normed Linear Space

Summary In this article, we described the contracting mapping on normed linear space. Furthermore, we applied that mapping to ordinary differential equations on real normed space. Our method is based on the one presented by Schwarz [29].

[1]  Czeslaw Bylinski.  Functions from a Set to a Set , 2004 .

[2]  Yasunari Shidama,et al.  Riemann Integral of Functions from R into Real Normed Space , 2011, Formaliz. Math..

[3]  Adam Naumowicz,et al.  Conjugate Sequences , Bounded Complex Sequences and Convergent Complex Sequences , 1996 .

[4]  Konrad Raczkowski.  Real Function Differentiability - Part II , 1991 .

[5]  Artur Kornilowicz.  Arithmetic Operations on Functions from Sets into Functional Sets , 2009, Formaliz. Math..

[6]  Yasunari Shidama,et al.  Partial Differentiation on Normed Linear Spaces Rn , 2007 .

[7]  Yasunari Shidama,et al.  The Continuous Functions on Normed Linear Spaces , 2004 .

[8]  Czeslaw Bylinski.  Functions and Their Basic Properties , 2004 .

[9]  Andrzej Trybulec,et al.  Binary Operations Applied to Functions , 1990 .

[10]  Agata Darmochwa.  Euclidean Space , 2018, How to Pass the FRACP Written Examination.

[11]  Noboru Endou,et al.  Definition of Integrability for Partial Functions from R to R and Integrability for Continuous Functions , 1994 .

[12]  Piotr Rudnicki,et al.  Abian's Fixed Point Theorem , 2007 .

[13]  Yasunari Shidama,et al.  The Uniform Continuity of Functions on Normed Linear Spaces , 2004 .

[14]  W. Kellaway,et al.  Complex Numbers , 2019, AMS/MAA Textbooks.

[15]  Wojciech A. Trybulec.  Vectors in Real Linear Space , 1990 .

[16]  Yasunari Shidama,et al.  Contracting Mapping on Normed Linear Space 1 , 2013 .

[17]  Konrad Raczkowski,et al.  Topological Properties of Subsets in Real Numbers , 1990 .

[18]  Józef Białas.  Properties of the Intervals of Real Numbers , 1993 .

[19]  Czeslaw Bylinski.  Some Basic Properties of Sets , 2004 .

[20]  Y. Shidama,et al.  Real Linear Space of Real Sequences Noboru Endou Gifu , 2004 .

[21]  Konrad Raczkowski.  Real Function Differentiability 1 , 1990 .

[22]  Yasunari Shidama,et al.  Completeness of the Real Euclidean Space , 2005 .

[23]  A. Kondracki.  Basic Properties of Rational Numbers , 1990 .

[24]  Jan Popio,et al.  Real Normed Space , 1991 .

[25]  Yasunari Shidama,et al.  More on Continuous Functions on Normed Linear Spaces , 2011, Formaliz. Math..

[26]  Edmund Woronowicz.  Relations and Their Basic Properties , 2004 .

[27]  Wojciech A. Trybulec.  Subspaces and Cosets of Subspaces in Real Linear Space , 1990 .

[28]  Yasunari Shidama,et al.  Differentiable Functions into Real Normed Spaces , 2011, Formaliz. Math..

[29]  Yasunari Shidama,et al.  More on the Continuity of Real Functions , 2011, Formaliz. Math..

[30]  G. Bancerek,et al.  Ordinal Numbers , 2003 .

[31]  Yasunari Shidama,et al.  Riemann Integral of Functions from R into n-dimensional Real Normed Space , 2012, Formaliz. Math..

[32]  Andrzej Trybulec,et al.  On the Sets Inhabited by Numbers 1 , 2003 .

[33]  Edmund Woronowicz.  Relations Defined on Sets , 1990 .

[34]  Konrad Raczkowski,et al.  Topological Properties of Subsets in Real Numbers 1 , 1990 .

[35]  Yasunari Shidama.  Riemann Integral of Functions from R into Real Banach Space 1 Keiko Narita Hirosaki-city Aomori , Japan Noboru Endou Gifu National College of Technology Japan , 2014 .

[36]  Rafał Kwiatek.  Factorial and Newton Coefficients Rafał Kwiatek Nicolaus , 1990 .

[37]  J. Harrison.  Formalized Mathematics , 1996 .

[38]  L. Schwartz.  Cours d'analyse , 1963 .

[39]  Yasumasa Suzuki,et al.  Banach Space of Bounded Real Sequences , 2004 .

[40]  Y. Shidama.  Banach Space of Bounded Linear Operators , 2003 .