In this paper, we study the fuzzy Ulam-Hyers-Rassias stability for two kinds of fuzzy fractional integral equations by employing the fixed point technique.

In 1940 and 1964, 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, Hyers solved this stability problem for linear mappings. According to Gruber 1978 this kind of stability problems are of the particular interest in probability theory and in ...

In this paper, we prove the Hyers-Ulam stability of the symmetric functionalequation $f(ph_1(x,y))=ph_2(f(x), f(y))$ in random normed spaces. As a consequence, weobtain some random stability results in the sense of Hyers-Ulam-Rassias.

In this paper, we use the denition of fuzzy normed spaces givenby Bag and Samanta and the behaviors of solutions of the additive functionalequation are described. The Hyers-Ulam stability problem of this equationis discussed and theorems concerning the Hyers-Ulam-Rassias stability of theequation are proved on fuzzy normed linear space.

Under what conditions does there exist a group homomorphism near an approximate group homomorphism? This question concerning the stability of group homomorphisms was posed by Ulam 1 . The case of approximately additive mappings was solved by Hyers 2 on Banach spaces. In 1950 Aoki 3 provided a generalization of the Hyers’ theorem for additive mappings and in 1978 Th. M. Rassias 4 generalized the...

One of the interesting questions concerning the stability problems of functional equations is as follows: when is it true that a mapping satisfying a functional equation approximately must be close to the solution of the given functional equation? Such an idea was suggested in 1940 by Ulam 1 . The case of approximately additive mappings was solved by Hyers 2 . In 1978, Rassias 3 generalized Hye...

Cădariu and Radu applied the fixed point method to the investigation of Cauchy and Jensen functional equations. In this paper, we adopt the idea of Cădariu and Radu to prove the Hyers-Ulam-Rassias stability of a functional equation of the square root spiral, f (√ r2 + 1 ) = f(r)+ tan−1(1/r).

In this paper, using the direct method we study the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equations (2 ) ( ) 6 ( )     f x y f x y f x and (3 ) ( ) 16 ( )     f x y f x y f x for the mapping f from normed linear space in to 2-Banach spaces.

In this paper, we establish the conditional Hyers-Ulam-Rassias stability of the generalized Jensen functional equation r f ( sx+ty r ) = s g(x) + t h(y) on various restricted domains such as inside balls, outside balls, and punctured spaces. In addition, we prove the orthogonal stability of this equation and study orthogonally generalized Jensen mappings on Balls in inner product spaces.

Aoki,T. , (1950) "On stability of the linear transformation in Banach spaces," Journal of the Mathematical Society of Japan, 2,64-66 Chang, S. and Kim,H. M. , (2002), On the Hyer-Ulam stability of a quadratic functional equations, J. Ineq. Appl. Math. , 33, 1-12. Chang,S. , Lee,E. H. and Kim,H. M. , (2003)On the Hyer-Ulam Rassias stability of a quadratic functional equations, Math. In...