61 research outputs found
Stability of a functional equation deriving from cubic and quartic functions
In this paper, we obtain the general solution and the generalized Ulam-Hyers
stability of the cubic and quartic functional equation
&4(f(3x+y)+f(3x-y))=-12(f(x+y)+f(x-y))
&+12(f(2x+y)+f(2x-y))-8f(y)-192f(x)+f(2y)+30f(2x)
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The Life and Work of D.H. Hyers, 1913-1997
The following is a sketch of the life and work of Donald Holmes Hyers, Professor Emeritus from the University of Southern California. The theorem put forth by Hyers in 1941 concerning linear functional equations has gained a great deal of interest over the past two decades. Hundreds of articles have been written citing his works, many of which have furthered the theorem. This paper contains a brief description of Hyers’ theorem, a biographical essay and an extensive bibliography of Hyers’ work and works citing the Hyers theorem or the D.H. Hyers–S.M. Ulam–Th.M. Rassias theorem or related subjects of almost the last three decades. The author of this paper is the grandson of D.H. Hyers
Approximate Homomorphisms of Ternary Semigroups
A mapping between ternary semigroups will be
called a ternary homomorphism if . In this paper,
we prove the generalized Hyers--Ulam--Rassias stability of mappings of
commutative semigroups into Banach spaces. In addition, we establish the
superstability of ternary homomorphisms into Banach algebras endowed with
multiplicative norms.Comment: 10 page
On the Stability Problem in Fuzzy Banach Space
We investigate the generalized Ulam-Hyers stability of the Cauchy functional equation and pose two open problems in fuzzy Banach space
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