STABILITY OF THE MONOMIAL FUNCTIONAL EQUATION IN QUASI NORMED SPACES

Title & Authors
STABILITY OF THE MONOMIAL FUNCTIONAL EQUATION IN QUASI NORMED SPACES
Mirmostafaee, Alireza Kamel;

Abstract
Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X $\small{\rightarrow}$ Y, which satisfies the inequality $\small{{\parallel}{\Delta}_x^nf(y)\;-\;n!f(x){\parallel}\;{\leq}\;\varphi(x,y)}$ for suitable control function $\small{\varphi}$, there is a unique monomial function M of degree n which is a good approximation for f in such a way that the continuity of $\small{t\;{\mapsto}\;f(tx)}$ and $\small{t\;{\mapsto}\;\varphi(tx,\;ty)}$ imply the continuity of $\small{t\;{\mapsto}\;M(tx)}$.
Keywords
quasi p-norm;monomial functional equation;fixed point alternative;Hyers-Ulam-Rassias stability;
Language
English
Cited by
1.
Recursive procedure in the stability of Fréchet polynomials, Advances in Difference Equations, 2014, 2014, 1, 16
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