Research Projects

Researchers have recently focused on the Hyers-Ulam-type stability, which guarantees a close exact solution in differential systems. This stability is applied to various models, such as the wave solution of a reaction-diffusion system, economic monopoly models, SIS epidemic models, and logistic equations. However, there is limited research on unbounded Hyers-Ulam stable operators. Hirasawa and Takeshi established results on unbounded closed operators, showing that an unbounded closed operator T from D(T) into K is Hyers-Ulam stable iff the range of T is closed, where H and K are Hilbert-spaces. The researchers aim to work on unbounded linear operators (closed and non-closed) along with non-linear operators. They aim to find sufficient conditions for the Hyers-Ulam stability of powers of T using spectral and resolvent elements of closed unbounded operators T on a Hilbert space H. They also aim to find necessary and sufficient conditions for general unbounded operators in Hilbert spaces to be Hyers-Ulam stable. The researchers also aim to explore the Hyers-Ulam stability of the (uniform/strong/weak) limit of Hyers-Ulam stable operators and the tensor product of two Hyers-Ulam stable operators in Hilbert spaces. The question of whether C₀-semigroup operators T(t) is Hyers-Ulam stable was raised at the International Conference on Ulam’s Type Stability, but it remains open. The researchers also aim to find its applications in complementarity problems.