Picard ' S Theorem by Douglas Bridges

The Constructive Implicit Function Theorem and Applications in Mechanics Douglas Bridges University of Waikato

We examine some ways of proving the Implicit Function Theorem and the Inverse Function Theorem within Bishop's constructive mathematics. Section 2 contains a new, entirely constructive proof of the Implicit Function Theorem. The paper ends with some comments on the application of the Implicit Function Theorem in classical mechanics.

A Constructive Proof of Gleason's Theorem

A Constructive Study of Landau's Summability Theorem

A summability theorem of Landau, which classically is a simple consequence of the uniform boundedness theorem, is examined within Bishop-style constructive mathematics. It is shown that the original theorem is nonconstructive, and that a natural weakening of the theorem is constructively equivalent to Ishihara’s principle BD-N. The paper ends with a number of results that, while not as strong a...

Solving fuzzy differential equations by using Picard method

In this paper,  The Picard method is proposed to solve the system of first-order fuzzy  differential equations  $(FDEs)$ with fuzzy initial conditions under generalized $H$-differentiability. Theexistence and uniqueness of the solution and convergence of theproposed method are proved in details. Finally, the method is illustrated by solving some examples.

Cycles and Bridges in Graphs

A bridge of a subgraph H in a graph G is either a subgraph consisting of an edge of E{G) — E(H) joining two vertices of H, or a subgraph induced in G by the vertices of a component K of G — V(H) together with the vertices of H which are adjacent to K. Bridges of the first type are called chords of H. A theory for bridges was first developed by Tutte [4] in 1966 (where they were called //-fragme...