77 research outputs found
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
The Fixed Point Method for Fuzzy Approximation of a Functional Equation Associated with Inner Product Spaces
Th. M. Rassias (1984) proved that the norm defined over a real vector space is induced by an inner product if and only if for a fixed integer β₯2,β=1βββ(1/)=1β2=β=1ββ2βββ(1/)=1β2 holds for all 1,β¦,β. The aim of this paper is to extend the applications of the fixed point alternative method to provide a fuzzy stability for the functional equation β=1(ββ(1/)=1β)==1(β)β((1/)=1) which is said to be a functional equation associated with inner product spaces
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)
Generalized Stabilities of Euler-Lagrange-Jensen (a,b)-Sextic Functional Equations in Quasi-Ξ²-Normed Spaces
The aim of this paper is to investigate generalized Ulam-Hyers stabilities of the following Euler-Lagrange-Jensen--sextic functional equation where , such that ; and , in quasi--normed spaces by using fixed point method. In particular, we prove generalized stabilities involving the sum of powers of norms, product of powers of norms and the mixed product-sum of powers of norms of the above functional equation in quasi--normed spaces by using fixed point method. A counter-example for a singular case is also indicated
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