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Ulam Stability Generalizations of 4th- Order Ternary Deriva- tions Associated to a Jmrassias Quartic Functional Equation on Frechet Algebras

Ali Ebadian
경북대학교 자연과학대학 수학과|2013.06|Kyungpook Mathematical Journal|제53권 제2호|pp. 233-245|DOI http://dx.doi.org/10.5666/KMJ.2013.53.2.233

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키워드

Ulam stabilityQuartic functional equationFrechet algebrasTernary Banach algebras4th- order ternary derivation.
주제분류수학

초록

Let A be a Banach ternary algebra over a scalar eld R or C and X be aternary Banach A-module. A quartic mapping D : (A, [ ]A) ! (X, [ ]X) is called a 4th-order ternary derivation if D([x, y, z]) = [D(x), y4, z4] + [x4,D(y), z4] + [x4, y4,D(z)] forall x, y, z 2 A. In this paper, we prove Ulam stability generalizations of 4th- order ternaryderivations associated to the following JMRassias quartic functional equation on frechetalgebras:f(kx + y) + f(kx - y) = k2[f(x + y) + f(x - y)]+ 2k2(k2 - 1)f(x) - 2(k2 - 1)f(y).

Abstract

Let A be a Banach ternary algebra over a scalar eld R or C and X be aternary Banach A-module. A quartic mapping D : (A, [ ]A) ! (X, [ ]X) is called a 4th-order ternary derivation if D([x, y, z]) = [D(x), y4, z4] + [x4,D(y), z4] + [x4, y4,D(z)] forall x, y, z 2 A. In this paper, we prove Ulam stability generalizations of 4th- order ternaryderivations associated to the following JMRassias quartic functional equation on frechetalgebras:f(kx + y) + f(kx - y) = k2[f(x + y) + f(x - y)]+ 2k2(k2 - 1)f(x) - 2(k2 - 1)f(y).

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