In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.
AbstractIn this paper, we obtain Hyers-Ulam stability of the functional equationsf (x + y, z + w) + f (x − y, z − w) = 2f (x, z) + 2f (y, w),f (x + y, z − w) + f (x − y, z + w) = 2f (x, z) + 2f (y, w)andf (x + y, z − w) + f (x − y, z + w) = 2f (x, z) − 2f (y, w)in 2-Banach spaces. The quadratic forms ax2 + bxy + cy2, ax2 + by2 and axy are solutions of the above functional equations, respectively.
AbstractThis research paper deals with general solution and the Hyers–Ulam stability of a new generalized n-variable mixed type of additive and quadratic functional equations in fuzzy modular spaces by using the fixed point method.
AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.
AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.
Hyers-Ulam stability of quadratic forms in 2-normed spaces
