In 1940, Ulam [1] proposed the famous Ulam stability problem of linear mappings. In 1941, Hyers [2] considered the case of approximately additive mappings f : E→ E′, where E and E′ are Banach spaces and f satisfies Hyers 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 : E→ E′ is the unique additive ...

In this paper, we establish some results for a Volterra–Hammerstein integral equation with modified arguments: existence and uniqueness, inequalities, monotony Ulam-Hyers-Rassias stability. We emphasize that many problems from the domain of symmetry are modeled by differential equations those approached in stability point view. literature, Fredholm, Volterra Hammerstein integrals symmetric kern...

In this paper, we obtain sufficient conditions for Hyers–Ulam and Hyers–Ulam–Rassias stability of an abstract second–order nonlinear dynamic equation on bounded time scales. An illustrative example is given to show the applicability theoretical results.