Ulam Stability of Operators

Janusz Brzdek has published numerous papers on Ulam’s type stability (e.g., of functional, difference, differential and integral equations), its applications and connections to other areas of mathematics. He has been editor of several books and special volumes focused on such subjects. He was the chairman of the organizing and/or scientific committees of several conferences on Ulam’s type stability and on functional equations and inequalities. Dorian Popa is the author of numerous papers on Ulam’s type stability of functional equations, differential equations, linear differential operators, and positive linear operators in approximation theory. Other papers deal with the connections of Ulam’s type stability with some topics of multivalued analysis (e.g., the existence of a selection of a multivalued operator satisfying a functional inclusion associated to a functional equation). Ioan Rasa has published papers on Ulam’s type stability of differential operators and several types of positive linear operators arising in approximation theory. He is author/co-author of many papers connecting Ulam’s stability with other areas of mathematics (functional analysis, approximation theory, differential equations). Raşa is co-author (with. F. Altomare et al.) of the book Markov Operators, Positive Semigroups and Approximation Processes, de Gruyter, 2014. Bing Xu has published many papers on Ulam’s type stability (e.g., of functional, difference, differential and integral equations), its applications and connections to iterative equations and multivalued analysis. Xu is co-author (with W. Zhang et al.) of the book Ordinary Differential Equations, Higher Education Press, 2014.

"Therefore, as the authors write in the Preface of this book, the aim of this book is not merely to present a survey of research papers dealing with the stability theory of functional equations, but rather to propose a somewhat new systematic approach to investigating Ulam stability. Some open problems are also stated, suggesting further possible exploration in the corresponding areas.This book consists of six chapters. Each of them has a short and informative abstract as well as a list of references." --Zentralblatt Math

• 1. Introduction to Ulam stability theory2. Operators in normed spaces3. Ulam stability of differential operators4. Best constant in Ulam stability5. Ulam stability of operators of polynomial form6. Non-stability theory