We argue that Ulam-Hyers stability concept is quite significant in realistic problems in numerical analysis, biology and economics. A generalization to nonlinear systems is proposed and applied to the logistic equation (both differential and difference), SIS epidemic model, Cournot model in economics and a reaction diffusion equation. To the best of our knowledge this is the first time Ulam-Hye...

We study the Hyers-Ulam stability theory of a four-variate Jensen-type functional equation by considering the approximate remainder φ and obtain the corresponding error formulas. We bring to light the close relation between the β-homogeneity of the norm on F *-spaces and the approximate remainder φ, where we allow p, q, r , and s to be different in their Hyers-Ulam-Rassias stability.

*Correspondence: [email protected] 1Department of Information Sciences, Toho University, Funabashi, 274-8501, Japan Full list of author information is available at the end of the article Abstract We introduce an alternative homomorphism with respect to binary operations and investigate the Ulam type stability problem for such a mapping. The obtained results apply to Ulam type stability proble...

The purpose of this paper is to determine the existence tripled fixed point results for symmetry system fractional hybrid delay differential equations. We obtain which support at least one solution our by applying theory. Similar types stability analysis are presented, including Ulam–Hyers, generalized Ulam–Hyers–Rassias, and Ulam–Hyers–Rassias. necessary stipulations obtaining proposed problem...

We study numerically the statistics of Poincaré recurrences for the Chirikov standard map and the separatrix map at parameters with a critical golden invariant curve. The properties of recurrences are analyzed with the help of a generalized Ulam method. This method allows us to construct the corresponding Ulam matrix whose spectrum and eigenstates are analyzed by the powerful Arnoldi method. We...

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...

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 1940, Ulam [13] proposed the Ulam stability problem of additive mappings. In the next year, Hyers [5] considered the case of approximately additive mappings f : E→ E′, where E and E′ are Banach spaces and f satisfies inequality ‖ f (x+ y)− f (x)− f (y)‖ ≤ ε for all x, y ∈ E. It was shown that the limit L(x) = limn→∞ 2−n f (2nx) exists for all x ∈ E and that L is the unique additive mapping s...