in this paper we investigate the generalized hyers-ulamstability of the following cauchy-jensen type functional equation$$qbig(frac{x+y}{2}+zbig)+qbig(frac{x+z}{2}+ybig)+qbig(frac{z+y}{2}+xbig)=2[q(x)+q(y)+q(z)]$$ in non-archimedean spaces

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The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach spaces. Hyers’ Theorem was generalized by Aoki 3 for additive mappings and by Th. M. Rassias 4 for linear mappings by considering an unbounded Cauchy difference. The paper of Th. M. ...

in this paper, we prove the generalized hyers-ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-archimedean $mathcal{l}$-fuzzy normed spaces.

In 1940 and in 1968 S. M. Ulam proposed the general problem:”When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. In 1941 D. H. Hyers solved this stability problem for linear mappings. In 1951 D. G. Bourgin was the second author to treat the same problem for additive mappings. According to...

We survey the recent results concerning the applications of power series method to the study of Hyers–Ulam stability of differential equations.

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-Archimedean $mathcal{L}$-fuzzy normed spaces.

In this paper, we prove the generalized Hyers–Ulam stability of a quadratic and quartic functional equation in intuitionistic fuzzy Banach spaces.

We prove the generalized Hyers-Ulam stability of the one-dimensional wave equation, u(tt) = c(2)u(xx), in a class of twice continuously differentiable functions.