Ulam Stability Generalizations of 4th- Order Ternary Derivations Associated to a Jmrassias Quartic Functional Equation on Fréchet Algebras

• Journal title : Kyungpook mathematical journal
• Volume 53, Issue 2,  2013, pp.233-245
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2013.53.2.233
Title & Authors
Ulam Stability Generalizations of 4th- Order Ternary Derivations Associated to a Jmrassias Quartic Functional Equation on Fréchet Algebras

Abstract
Let $\small{\mathcal{A}}$ be a Banach ternary algebra over a scalar field R or C and $\small{\mathcal{X}}$ be a ternary Banach $\small{\mathcal{A}}$-module. A quartic mapping $\small{D\;:\;(\mathcal{A},[\;]_{\mathcal{A}}){\rightarrow}(\mathcal{X},[\;]_{\mathcal{X}})}$ is called a $\small{4^{th}}$- order ternary derivation if $\small{D([x,y,z])=[D(x),y^4,z^4]+[x^4,D(y),z^4]+[x^4,y^4,D(z)]}$ for all $\small{x,y,z{\in}\mathcal{A}}$. In this paper, we prove Ulam stability generalizations of $\small{4^{th}}$- order ternary derivations associated to the following JMRassias quartic functional equation on fr$\small{\acute{e}}$che algebras: $\small{f(kx+y)+f(kx-y)=k^2[f(x+y)+f(x-y)]+2k^2(k^2-1)f(x)-2(k^2-1)f(y)}$.
Keywords
Ulam stability;Quartic functional equation;Fr$\small{\acute{e}}$chet algebras;Ternary Banach algebras;$\small{4^{th}}$- order ternary derivation;
Language
English
Cited by
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