Browsing by Author "Zafer, A."
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Article Matrix Measure Approach To Lyapunov-Type Inequalities for Linear Hamiltonian Systems With Impulse Effect(Academic Press inc Elsevier Science, 2016) Kayar, Z.; Zafer, A.We present new Lyapunov-type inequalities for Hamiltonian systems, consisting of 2n-first-order linear impulsive differential equations, by making use of matrix measure approach. The matrix measure estimates of fundamental matrices of linear impulsive systems are crucial in obtaining sharp inequalities. To illustrate usefulness of the inequalities we have derived new disconjugacy criteria for Hamiltonian systems under impulse effect and obtained new lower bound estimates for eigenvalues of impulsive eigenvalue problems. (C) 2016 Elsevier Inc. All rights reserved.Article Lyapunov-Type Inequalities for Higher-Dimensional Hamiltonian Systems on Time Scales: Anew Generalized Vector Zero Approach(Academic Press inc Elsevier Science, 2022) Kayar, Z.; Zafer, A.By 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.
