Hyers-Ulam Stability of Euler’s Equation in the Calculus of Variations

Hyers-Ulam Stability of Fibonacci Functional Equation

Hyers-Ulam stability of Volterra integral equation

We will apply the successive approximation method forproving the Hyers--Ulam stability of a linear integral equation ofthe second kind.

Hyers–ulam Stability of a Polynomial Equation

The aim of this paper is to prove the stability in the sense of Hyers–Ulam stability of a polynomial equation. More precisely, if x is an approximate solution of the equation x + αx + β = 0, then there exists an exact solution of the equation near to x.

Hyers-Ulam Stability of Nonlinear Integral Equation

Hyers-Ulam stability of K-Fibonacci functional equation

Let denote by Fk,n the nth k-Fibonacci number where Fk,n = kFk,n−1+Fk,n−2 for n 2 with initial conditions Fk,0 = 0, Fk,1 = 1, we may derive a functionalequation f(k, x) = kf(k, x − 1) + f(k, x − 2). In this paper, we solve thisequation and prove its Hyere-Ulam stability in the class of functions f : N×R ! X,where X is a real Banach space.