Leader: Prof. Dr. Zsolt Páles, full professor, member of the Hungarian Academy of Sciences
General methods of the theory of functional equations. Functional equations on algebraic structures. Polynomials and exponential polynomials on topological groups and on hypergroups. Spectral analysis and spectral synthesis methods for the solution of functional equations. Conditional functional equations, extension theorems. Regularity theory of non-iterative and iterative functional equations. Reduction of functional equations to differential equations. Stability theory of functional equations. Iterative methods, applications of fixed point theory and invariant means. Applications of functional equations in probability theory, in information theory, in economics and in social sciences. Theory of functional inequalities, generalizations of convexity and monotonicity. Convexity with respect to Chebyshev systems and Beckenbach systems. Stability of convexity. Theory of means. Characterization and invariance problems. Equality, homogeneity and comparison problems in various classes of means. Nonsmooth and convex analysis, theory of generalized derivatives. Necessary and sufficient conditions for extremum problems. Problems of calculus of variations and optimal control.