Kayar, Z.Zafer, A.2025-05-102025-05-1020220022-247X1096-081310.1016/j.jmaa.2022.1261772-s2.0-85127180507https://doi.org/10.1016/j.jmaa.2022.126177https://hdl.handle.net/20.500.14720/14246Zafer, Agacik/0000-0001-8446-1223By defining a generalized zero for a vector-valued function and making use of it, we obtain new Lyapunov-type inequalities for a general linear 2n x2n Hamiltonian system z(Delta) = JH(t) z of dynamic equations on time scales. The new definition is an extension from scalar functions to valued functions with respect to a matrix. Our approach in the proofs is different in the sense that several tools such as matrix measure, exponential bound function, and Dini derivatives on time scales are employed. As a classical application, we also show how the new inequalities are useful for related boundary value problems. (C) 2022 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessHamiltonian SystemTime ScalesLyapunov InequalityMatrix MeasureDini DerivativesArticle