The Fréchet functional equation with application to the stability of certain operators

We present a new approach to the classical Frechet functional equation. The results are applied to the study of Hyers-Ulam stability of Bernstein-Schnabl operators.

[1]  Dorian Popa,et al.  On the stability of the linear differential equation of higher order with constant coefficients , 2010, Appl. Math. Comput..

[2]  F. Altomare,et al.  On Bernstein–Schnabl Operators on the Unit Interval , 2008 .

[3]  Wlodzimierz Fechner,et al.  Stability of a composite functional equation related to idempotent mappings , 2011, J. Approx. Theory.

[4]  P. K. Sahoo,et al.  Mean Value Theorems and Functional Equations , 1998 .

[5]  Ioan Raşa,et al.  On the Hyers–Ulam stability of the linear differential equation , 2011 .

[6]  R. Agarwal,et al.  Stability of functional equations in single variable , 2003 .

[7]  Kenneth J. Palmer,et al.  Shadowing in Dynamical Systems , 2000 .

[8]  G. Pólya,et al.  Aufgaben und Lehrsätze aus der Analysis: Erster Band: Reihen · Integralrechnung Funktionentheorie , 1925 .

[9]  Jacek Chudziak,et al.  Approximate solutions of the Golab-Schinzel equation , 2005, J. Approx. Theory.

[10]  Hiroyuki Takagi,et al.  ESSENTIAL NORMS AND STABILITY CONSTANTS OF WEIGHTED COMPOSITION OPERATORS ON C(X) , 2003 .

[11]  J. M. Almira,et al.  On solutions of the Fréchet functional equation , 2007 .

[12]  B Démidovitch,et al.  Eléments de calcul numérique , 1973 .

[13]  M. Kuczma Functional equations in a single variable , 1968 .

[14]  T. Miura,et al.  HYERS-ULAM STABILITY OF A CLOSED OPERATOR IN A HILBERT SPACE , 2006 .

[15]  George Isac,et al.  Stability of Functional Equations in Several Variables , 1998 .