# “Lyapunov Inequalities and Applications”, the book by Prof. Dr. Abdullah Özbekler, Faculty Member of Atılım University Department of Mathematics, is now published under Springer Publishing 17.05.2021

Inequalities are a cornerstone in all fields and applications of mathematics. Among some of the famous inequalities, Lyapunov-type inequalities have been extensively studied in recent years. This is due to the fact that the derivation of these inequalities requires classical analysis and may be applied to a wider spectrum of mathematics. The book provides an up-to-date explanation of Lyapunov-type inequalities and examines these inequalities for different types of ordinary differential equations and systems, partial differential equations, fractional differential equations, difference equations, and dynamic equations on time scales for various scenarios.

With the extensive literature on Lyapunov type inequalities summarized and organized, this study drafts the latest developments on the subject. With its elegant and didactic style, this study provides the reader with the underlying concepts of Lyapunov-type inequalities, the manner in which they have evolved, and the kinds of problems that call for them.

The study begins with the basic applications of Lyapunov inequalities, which are followed by double-digit, single-digit, and higher-order boundary value problems; Lyapunov and Hartman type inequalities; linear, nonlinear and quasi-linear differential equation systems; recent developments in Lyapunov-type inequalities; partial differential equations; linear difference equations; and Lyapunov-type inequalities for linear, quasi-linear and nonlinear dynamic equations on time scales, as well as linear Hamiltonian dynamical systems.

Senior undergraduate students and graduate students of mathematics, engineering, and science will benefit most from this book, as well as researchers in the areas of ordinary differential equations, partial differential equations, difference equations, and dynamic equations.  Some background in calculus, ordinary and partial differential equations, and difference equations is recommended for full enjoyment of the content.

The author aims to present a clear and regular review of the concept of Lyapunov-type inequalities behind the development of mathematics as well as application techniques. The text material in the book is presented in a readable and mathematically complete format.

The book is available on the Springer Publishing website.