Introduction A classical question in the theory of functional equations is “when is it true that a mapping, which approximately satisfies a functional equation, must be somehow close to an exact solution of the equation?”. Such a problem, called a stability problem of the functional equation, was formulated by Ulam [1] in 1940. In the next year, Hyers [2] gave a partial solution of Ulam’s probl...

In this work, we give a product Nyström method for solving a Fredholm functional integral equation (FIE) of the second kind. With this method solving FIE reduce to solving an algebraic system of equations. Then we use some theorems to prove the existence and uniqueness of the system. Finally we investigate the convergence of the method.

In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u. We proved the blow up of solutions in finite time by using modified energy functional method.

Using the Hyers-Ulam-Rassias stability method, weinvestigate isomorphisms in Banach algebras and derivations onBanach algebras associated with the following generalized additivefunctional inequalitybegin{eqnarray}|af(x)+bf(y)+cf(z)|  le  |f(alpha x+ beta y+gamma z)| .end{eqnarray}Moreover, we prove the Hyers-Ulam-Rassias stability of homomorphismsin Banach algebras and of derivations on Banach ...

In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam stability of the new generalized mixed type additive and quadratic functional equation in fuzzy normed space. Mathematics Subject Classification 39B55, 39B52, 39B82