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An Invitation to the Study of a Uniqueness Problem

In: Nonlinear Analysis and Global Optimization

Author

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  • Biagio Ricceri

    (University of Catania)

Abstract

In this very short chapter, we provide a strong motivation for the study of the following problem: given a real normed space E, a closed, convex, unbounded set X ⊆ E, and a function f : X → X, find suitable conditions under which, for each y ∈ X, the function x → ∥ x − f ( x ) ∥ − ∥ y − f ( x ) ∥ $$\displaystyle x\to \|x-f(x)\|-\|y-f(x)\| $$ has at most one global minimum in X.

Suggested Citation

  • Biagio Ricceri, 2021. "An Invitation to the Study of a Uniqueness Problem," Springer Optimization and Its Applications, in: Themistocles M. Rassias & Panos M. Pardalos (ed.), Nonlinear Analysis and Global Optimization, pages 445-448, Springer.
  • Handle: RePEc:spr:spochp:978-3-030-61732-5_21
    DOI: 10.1007/978-3-030-61732-5_21
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