On Stability of the Functional Equations Having Relation With a Multiplicative Derivation

APPROXIMATE BI-HOMOMORPHISMS AND BI-DERIVATIONS IN C*-TERNARY ALGEBRAS

“…Moreover, letting l = 0 and passing the limit m → ∞ in (18), we get the desired inequality for f and H.…”

“…Gǎvruta [12] obtained the generalized result of Rassias's theorem which allows the Cauchy difference to be controlled by a general unbounded function. During the past two decades, a number of papers and research monographs have been published on various generalizations and applications of the generalized Hyers-Ulam stability to a number of functional equations and mappings, for example, Cauchy-Jensen mappings, k-additive mappings, invariant means, multiplicative mappings, bounded nth differences, convex functions, generalized orthogonality mappings, Euler-Lagrange functional equations, differential equations, and Navier-Stokes equations (see [4]- [7], [11,12,14], [18]- [21], [23], [25]- [31], [36,37]). The instability of characteristic flows of solutions of partial differential equations is related to the Ulam stability of functional equations [24,33].…”