Generalizations. The Method of Invariant Means

  • Donald H. Hyers
  • George Isac
  • Themistocles M. Rassias
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 34)


As was seen above in Corollary 1.2, there is no difficulty in generalizing Theorem 1.1 to mappings from a commutative semigroup S to a Banach space. We note here that the property of commutativity was used only in demonstrating the additivity of the mapping g.


Banach Space Functional Equation Additive Function Banach Lattice Topological Vector Space 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Donald H. Hyers
  • George Isac
    • 1
  • Themistocles M. Rassias
    • 2
  1. 1.Department of Mathematics and Computer ScienceRoyal Military College of CanadaKingstonCanada
  2. 2.Department of MathematicsNational Technical University of AthensAthensGreece

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