Paisan Nakmahachalasint

On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations

In this paper, the mixed-type linear and Euler-Lagrange-Rassias functional equations introduced by J. M. Rassias is generalized to the following n-dimensional functional equation: f(∑i=1nxi)

Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias Stabilities of an Additive Functional Equation in Several Variables

It is well known that the concept of Hyers-Ulam-Rassias stability was originated by Th. M. Rassias (1978) and the concept of Ulam-Gavruta-Rassias stability was originated by J. M. Rassias (1982–1989) and by P. Găvruta (1999). In this paper, we give results concerning these two stabilities.

CLUSTER DISTRIBUTION IN MEAN-FIELD PERCOLATION : SCALING AND UNIVERSALITY

The partition function of the finite

Generalized stability of classical polynomial functional equation of order n

1+\epsilon

ON THE STABILITY OF A MIXED-TYPE LINEAR AND QUADRATIC FUNCTIONAL EQUATION

state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are manifest, including scaling behavior and the emergence of the spanning cluster. The predictions are compared with simulations. Agreement is found to be good, although convergence between theory and numerical results as the system size is increased is, in some cases, unaccountably slow.

An n-dimensional mixed-type additive and quadratic functional equation and its stability

We study a general n th order polynomial functional equation Δynf(x)=n!f(y) on linear spaces and prove its generalized stability.MSC:39B52, 39B82.

On the Stability of a Cubic Functional Equation

We give the general solution of the n-dimensional mixed-type linear and quadratic functional equation, ( n − 2 m − 2 ) f ( n ∑ i=1 xi ) + ( n − 2 m − 1 ) n ∑ i=1 f (xi ) = ∑ {i1,...,im }∈Pm f ( m ∑