Generalized Abel Equation

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


Generalized Abel equations have the form
$$ \phi \left( {F\left( x \right)} \right) = g\left( {x,\phi \left( x \right)} \right) $$
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).


Local Solution Homogeneous Equation Unique Fixed Point Local Solvability Global Solvability 
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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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