Developments in Functional Equations and Related Topics

This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering.

Key topics covered in this book include:

• Quasi means
• Approximate isometries
• Functional equations in hypergroups
• Stability of functional equations
• Fischer-Muszély equation
• Haar meager sets and Haar null sets
• Dynamical systems
• Functional equations in probability theory
• Stochastic convex ordering
• Dhombres functional equation
• Nonstandard analysis and Ulam stability

This book is dedicated in memory of Staniłsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.

• set-valued functional equations
• K-metric spaces
• Perov type fixed point theorems
• Haar meager sets
• linear functional equations
• inequalities in a single variable
• Ulam’s stability of linear operators
• stability of nearisometries
• Isometric approximation
• indicator plurality function
• ring of formal power series
• Fischer-Muszély additivity
• dynamical system
• Haar null sets
• Homomorphisms from Functional Equations
• stochastic convex ordering theorems
• Dhombres functional equation
• stability problems on hypergroups
• compact-open topology
• Stability of systems

• Department of Mathematics, Pedagogical University of Cracow, Kraków,, Poland

  Janusz Brzdęk

• Faculty of Applied Mathematics, AGH University of Science and Technology, Kraków, Poland

  Krzysztof Ciepliński

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

  Themistocles M. Rassias