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Generalized Abel Equation

  • Genrich Belitskii
  • Vadim Tkachenko
Chapter
  • 233 Downloads
Part of the Operator Theory: Advances and Applications book series (OT, volume 144)

Abstract

Generalized Abel equations have the form
$$ \phi \left( {F\left( x \right)} \right) = g\left( {x,\phi \left( x \right)} \right) $$
(3.0.1)
where F : M → M is a given mapping, g(x, y) is a given function of x ∈ M, y∈ℝ and φ(x) is a solution. The Abel, Schröder and cohomological equations are particular cases of (3.0.1). Our aim is to find solvability conditions and, if possible, to describe the set of solutions of equation (3.0.1) in terms of F(x) and g(x, y).

Keywords

Local Solution Homogeneous Equation Unique Fixed Point Local Solvability Global Solvability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel AG 2003

Authors and Affiliations

  • Genrich Belitskii
    • 1
  • Vadim Tkachenko
    • 1
  1. 1.Department of MathematicsBen Gurion University of the NegevBeer ShevaIsrael

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