On Hilbert Golab-Schinzel type functional equation

Document Type : Research Paper


1 Faculty of Sciences, IBN TOFAIL University, KENITRA, Morocco

2 Moulay Ismail University, ENSAM, Meknes, Morocco


Let $X$ be a vector space over a field $K$ of real or complex numbers. We will prove the superstability of the following Go{\l}\c{a}b-Schinzel type equation
f(x+g(x)y)=f(x)f(y), x,y\in X,
where $f,g:X\rightarrow K$ are unknown functions (satisfying some assumptions). Then we generalize the superstability result for this equation with values in the field of complex numbers to the case of an arbitrary Hilbert space with the Hadamard product. Our result refers to papers by Chudziak and Tabor [J. Math. Anal. Appl. 302 (2005) 196-200], Jab\l o'{n}ska [Bull. Aust. Math. Soc. 87 (2013), 10-17] and Rezaei [Math. Ineq. Appl., 17 (2014), 249-258].


Volume 6, Issue 2 - Serial Number 2
January 2015
Pages 149-159
  • Receive Date: 27 November 2014
  • Revise Date: 04 January 2015
  • Accept Date: 01 June 2015
  • First Publish Date: 20 November 2015