Plenary Lecture
Ulam Stability and Fixed Points of Operators in Function Spaces
Professor Janusz Brzdek
Department of Mathematics
Pedagogical University of Cracow
Poland
E-mail: jbrzdek@up.krakow.pl
Abstract: The following natural question arises in many areas of scientific investigations: what errors we commit replacing the exact solutions to some equations by functions that satisfy those equations only approximately (or vice versa). Some efficient tools to evaluate those errors can be found in the theory of Ulam stability. The issue of Ulam stability of an equation can be very roughly expressed in the following way: when must a function satisfying an equation approximately (in some sense) be close (in a given way) to an exact solution to the equation? The problem of such stability was formulated for the first time by Ulam in 1940 for homomorphisms of metric groups; a solution to it was published a year later by Hyers for Banach spaces. It has been shown that there are very close connections between some problems in Ulam stability and the fixed point theory, especially for nonlinear operators in function spaces. We discuss several such connections on various examples.
Brief Biography of the Speaker: Professor at Department of Mathematics of Pedagogical University of Cracow, Poland. Major research interests: Ulam's type stability (e.g., of difference, differential, functional and integral equations and operators), fixed point theory, functional equations and inequalities with their applications, real and functional analysis. Author of more than 120 published papers and one book (Elsevier). Chairman of the Scientific Committee of the series of conferences: International Conference on Functional Equations and Inequalities (ICFEI) and Chairman of the Organizing Committees of 10th (2005), 11th (2006), 12th (2008), 13th (2009), 14th (2011), 15th (2013), and 16th (2015) ICFEIs. Chairman of the Scientific Committee of Conference on Ulam's Type Stability (CUTS) in Ustro\'n (Poland, June 2-6, 2014) and Cluj-Napoca (Romania, July 4-9, 2016). Member of the Programm or Scientific Committees of numerous other international conferences. Coeditor of three monographs (Springer, Banach Center Publications). Lead Guest Editor of several special issues of Abstract and Applied Analysis, Journal of Function Spaces (formerly: Journal of Function Spaces and Applications), and Discrete Dynamics in Nature and Society. Editor of several international journals, plenary speaker of several international conferences, supervisor of five promoted PhD students.