INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, v. 8, no. 1, page. 1-9
In this paper, we solve the quadratic alpha-functional equations2f(x) + 2f(y) = f(x + y) + alpha(-2) f(alpha(x - y)), (0.1)where a is a fixed non-Archimedean number with a(-2) not equal 3. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the functional equation (0.1) in non-Archimedean Banach spaces.