In this paper, we investigate the stability problems for a functional equation f(ax + y) + af(x − y) − a2+3a 2 f(x) −a(a−1) 2 f(−x)− f(y) − af(−y) = 0 by using the fixed point method. Mathematics Subject Classification: Primary 39B82, 39B62; Secondary 47H10

we have developed a three level implicit method for solution of the helmholtz equation. using the cubic spline in space and nite dierence in time directions. the approach has been modied to drive numerov type nite dierence method. the method yield the tri- diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. stability and error estimation of the...

In this paper, we prove the generalized Hyers–Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x + 2y) + f(x− 2y) = 4f(x + y) + 4f(x− y)− 6f(x) + f(2y) + f(−2y)− 4f(y)− 4f(−y) in non-Archimedean Banach spaces.

and Applied Analysis 3 Definition 1.4. A sequence {xk} in an n-normed space X is said to converge to some x ∈ X in the n-norm if lim k→∞ ∥ ∥xk − x, y2, . . . , yn ∥ ∥ 0, 1.4 for every y2, . . . , yn ∈ X. Definition 1.5. A sequence {xk} in an n-normed space X is said to be a Cauchy sequence with respect to the n-norm if lim k,l→∞ ∥ ∥xk − xl, y2, . . . , yn ∥ ∥ 0, 1.5 for every y2, . . . , yn ∈ X...

In this article, we introduce a class of the generalized mixed additive, quadratic and quartic functional equations and obtain their common solutions. We also investigate the stability of such modified functional equations in the non-Archimedean normed spaces by a fixed point method.