Differentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces

Differentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces In this article, we define and develop differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [16] and [17]).

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

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

[3]  Kazimierz Kuratowski,et al.  LOCALLY CONNECTED SPACES , 1972 .

[4]  Yasunari Shidama,et al.  The Real Vector Spaces of Finite Sequences are Finite Dimensional , 2009, Formaliz. Math..

[5]  Jarosław Kotowicz,et al.  Convergent Sequences and the Limit of Sequences , 2004 .

[6]  Agata Darmochwa,et al.  Topological Spaces and Continuous Functions , 1990 .

[7]  A. Trybulec.  Domains and Their Cartesian Products , 1990 .

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

[9]  Jan Mycielski.  Sur le coloriage des graphs , 1955 .

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

[11]  Karol Pąk,et al.  Basic Properties of the Rank of Matrices over a Field , 2007 .

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

[13]  J. Conway.  On Numbers and Games , 1976 .

[14]  Grzegorz Bancerek,et al.  Bounds in Posets and Relational Substructures 1 , 1997 .

[15]  Xiquan Liang,et al.  Some Properties of Some Special Matrices , 2005 .

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

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

[18]  Yasunari Shidama,et al.  The Cauchy-Riemann Differential Equations of Complex Functions , 2009, Formaliz. Math..

[19]  Zbigniew Karno,et al.  The Lattice of Domains of an Extremally Disconnected Space 1 , 1992 .

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

[21]  Konrad Raczkowski,et al.  Equivalence Relations and Classes of Abstraction 1 , 1990 .

[22]  Wojciech A. Trybulec.  Basis of Real Linear Space , 1990 .

[23]  Michael Larsen,et al.  The fractional chromatic number of mycielski's graphs , 1995, J. Graph Theory.

[24]  Jesse Alama,et al.  The Rank+Nullity Theorem , 2007 .

[25]  Karol Pak,et al.  Linear Transformations of Euclidean Topological Spaces , 2011, Formaliz. Math..

[26]  Karol Pak.  Linear Map of Matrices , 2008, Formaliz. Math..

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

[28]  Yatsuka Nakamura,et al.  Metric Spaces as Topological Spaces - Fundamental Concepts , 1991 .

[29]  W. Rudin.  Principles of mathematical analysis , 1964 .

[30]  Wojciech A. Trybulec.  Non-contiguous Substrings and One-to-one Finite Sequences , 1990 .

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

[32]  Grzegorz Bancerek,et al.  Segments of Natural Numbers and Finite Sequences , 1990 .

[33]  Zbigniew Karno,et al.  Separated and Weakly Separated Subspaces of Topological Spaces , 1991 .

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

[35]  Karol Pak.  Solutions of Linear Equations , 2008, Formaliz. Math..

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

[37]  Krzysztof Hryniewiecki,et al.  Basic Properties of Real Numbers , 2004 .

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

[39]  Grzegorz Bancerek,et al.  Product of Families of Groups and Vector Spaces , 1992 .

[40]  Wojciech A. Trybulec.  Linear Combinations in Vector Space , 1990 .

[41]  Jaross Law Kotowicz.  Real Sequences and Basic Operations on Them , 1989 .

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

[43]  Robert Milewski,et al.  Associated Matrix of Linear Map , 1996 .

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

[45]  Wojciech A. Trybulec.  BASIS FOR A VECTOR SPACE , 1990 .

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

[47]  Wojciech A. Trybulec.  Subspaces and Cosets of Subspaces in Vector Space , 1990 .

[48]  Czes Law Byli´nski,et al.  Finite Sequences and Tuples of Elements of a Non-empty Sets , 1990 .

[49]  Piotr Rudnicki.  Dilworth's Decomposition Theorem for Posets , 2009, Formaliz. Math..

[50]  G. Bancerek.  The Fundamental Properties of Natural Numbers , 1990 .

[51]  Wojciech A. Trybulec.  Linear Combinations in Real Linear Space , 1990 .

[52]  Karol Pak,et al.  Basic Properties of Metrizable Topological Spaces , 2009, Formaliz. Math..

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

[54]  Hiroshi Imura,et al.  The Differentiable Functions on Normed Linear Spaces , 2004 .

[55]  Jaroslaw Kotowicz,et al.  Functions and finite sequences of real numbers , 1993 .

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

[57]  Yasunari Shidama,et al.  Algebra of Vector Functions , 1992 .

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