The Hyers-Ulam stability problems of functional equations go back to 1940 when S. M. Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group see 1 . A partial answer was given by Hyers et al. 2, 3 under the assumption that the target space of the involved mappings is a Banach space. After the result of Hyers, Aoki 4 , and Bourgin 5, 6 dealt with this pro...

In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C-ternary ring homomorphisms associated to the Trif functional equation d · C d−2f( x1 + · · ·+ xd d ) + C d−2 d ∑

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 ...

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...

This paper deals with the existence, uniqueness, and Ulam-stability outcomes for $\Xi$-Hilfer fractional fuzzy differential equations impulse. Further, by using techniques of nonlinear functional analysis, we study Ulam-Hyers-Rassias stability.

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...

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...

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...

in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...