Functional equations and group substitutions (original) (raw)

Abstract

Motivated by some investigations of Babbage and a method of solving certain functional equations arising in competition problems, we investigate a class of functional equations and prove a local existence and uniqueness theorem for them. The main tools of the proof are the Inverse Function Theorem and the Global Existence and Uniqueness Theorem.

Key takeaways

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  1. The paper proves local existence and uniqueness for a class of functional equations.
  2. It utilizes the Inverse Function Theorem and Global Existence and Uniqueness Theorem for the proof.
  3. The functional equations involve known functions F, g1, ..., gn, and an unknown f.
  4. Substitutions create systems of equations, solvable using linear algebra techniques.
  5. Applications include corollaries for linear and nonlinear functional equations with differentiable functions.

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