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Ulam Type Stability

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  • © 2019

Overview

  • Presents up-to-date research and information on Ulam’s stability of linear and nonlinear operators
  • Includes a number of open problems
  • Features a variety of approaches for problems that lack stability

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About this book

This book is an outcome of two Conferences on Ulam Type Stability (CUTS) organized in 2016 (July 4-9, Cluj-Napoca, Romania) and in 2018 (October 8-13, 2018, Timisoara, Romania). It presents up-to-date insightful perspective and very resent research results on Ulam type stability of various classes of linear and nonlinear operators; in particular on the stability of many functional equations in a single and several variables (also in the lattice environments, Orlicz spaces, quasi-b-Banach spaces, and 2-Banach spaces) and some orthogonality relations (e.g., of Birkhoff–James). A variety of approaches are presented, but a particular emphasis is given to that of fixed points, with some new fixed point results and their applications provided. Besides these several other topics are considered that are somehow related to the Ulam stability such as: invariant means, geometry of Banach function modules, queueing systems, semi-inner products and parapreseminorms, subdominant eigenvalue location of a bordered diagonal matrix and optimal forward contract design for inventory. New directions and several open problems regarding stability and non-stability concepts are included.

Ideal for use as a reference or in a seminar, this book is aimed toward graduate students, scientists and engineers working in functional equations, difference equations, operator theory, functional analysis, approximation theory, optimization theory, and fixed point theory who wish to be introduced to a wide spectrum of relevant theories, methods and applications leading to interdisciplinary research. It advances the possibilities for future research through an extensive bibliography and a large spectrum of techniques, methods and applications.

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Table of contents (21 chapters)

Editors and Affiliations

  • Department of Applied Mathematics, AGH University of Science and Technology, Krakow, Poland

    Janusz Brzdęk

  • Department of Mathematics, Technical University of Cluj-Napoca, Cluj-Napoca, Romania

    Dorian Popa

  • Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

About the editors

​Janusz Brzdek has published numerous papers on Ulam 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 type stability and on functional equations and inequalities.

Dorian Popa is the author of numerous papers on Ulam 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 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).

Themistocles M. Rassias published more than 300 papers, 10 research books and 45 edited volumes in research Mathematics as well as 4 textbooks in Mathematics (in Greek) for university students. His research work has received more than 15,000 citations according to Google Scholar and more than 4,900 citations according to MathSciNet. His h-index is 44. He serves as a member of the Editorial Board of several international mathematical journals. His publications have strongly influenced the development of the theory of Ulam stability.

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