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On the Asymptotic Behavior of Solutions to General Linear Functional Equations

In: Nonlinear Analysis

Author

Listed:
  • B. Paneah

    (Technion—Israel Institute of Technology)

Abstract

This is a survey of the author’s results (Paneah in Aequ. Math. 74(1–2):119–157, 2007; Paneah in Grazer Math. Ber. 351:129–138, 2007; Paneah in Banach J. Math. Anal. 1(1):56–65, 2007; Paneah in Russ. J. Math. Phys. 15(2):291–296, 2008; Paneah in Publ. Math. (Debr.) 75(1–2):251–261, 2009) relating to the asymptotic behavior of approximate solutions to the functional equations , H ε =O(ε), depending on a parameter ε→0 with This behavior, as it is shown in the above works, is described by the relation $$F=\varPhi +O(\varepsilon). $$ Here the function Φ does not depend on ε and belongs to the kernel of the one-dimensional functional operator (restriction of the operator to some one-dimensional submanifold Γ⊂D subject to determining).

Suggested Citation

  • B. Paneah, 2012. "On the Asymptotic Behavior of Solutions to General Linear Functional Equations," Springer Optimization and Its Applications, in: Panos M. Pardalos & Pando G. Georgiev & Hari M. Srivastava (ed.), Nonlinear Analysis, edition 127, chapter 0, pages 525-537, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-3498-6_33
    DOI: 10.1007/978-1-4614-3498-6_33
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