On the uniqueness of continuous solutions of functional equations

Volume 60 / 1995

Bolesław Gaweł Annales Polonici Mathematici 60 (1995), 231-239 DOI: 10.4064/ap-60-3-231-239

Abstract

We consider the problem of the vanishing of non-negative continuous solutions ψ of the functional inequalities (1)   ψ(f(x)) ≤ β(x,ψ(x)) and (2)   α(x,ψ(x)) ≤ ψ(f(x)) ≤ β(x,ψ(x)), where x varies in a fixed real interval I. As a consequence we obtain some results on the uniqueness of continuous solutions φ :I → Y of the equation (3)  φ(f(x)) = g(x,φ(x)), where Y denotes an arbitrary metric space.

Authors

  • Bolesław Gaweł

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