Functional Equations: Results and Advances
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The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century. This is due to the fact that the mathematical applications increased the number of investigations of newer and newer types of functional equations. At the same time, the self-development of this theory was also very fruitful. The material of this volume reflects very well the complexity and applicability of the most active research fields. The results and methods contained give a representative crossection of what is recently happening in the theory of functional equations.
PrefacePt. IClassical Functional Equations and Inequalities1On some trigonometric functional inequalities3On the continuity of additive-like functions and Jensen convex functions which are Borel on a sphere17Note on a functional-differential inequality21A characterization of stationary sets for the class of Jensen convex functions25On the characterization of Weierstrass's sigma function29On a Mikusinski-Jensen functional equation81Pt. IIStability of Functional Equations89Stability of the multiplicative Cauchy equation in ordered fields91On approximately monomial functions99Les operatures de Hyers113Geometrical aspects of stability123Pt. IIIFunctional Equations in One Variable and Iteration Theory133On semi-conjugacy equation for homeomorphisms of the circle135A survey of results and open problems on the Schilling equation159Properties of an operator acting on the space of bounded real functions and certain subspaces175Pt. IVComposite Functional Equations and Theory of Means187A Matkowski-Suto type problem for quasi-arithmetic means of order [alpha]189An extension theorem for conjugate arithmetic means201Homogeneous Cauchy mean values209On invariant generalized Beckenbach-Gini means219Final part of the answer to a Hilbert's question231Pt. VFunctional Equations on Algebraic Structures243A generalization of d'Alembert's functional equation245About a remarkable functional equation on some restricted domains249On discrete spectral synthesis263Hyers theorem and the cocycle property275Pt. VIFunctional Equations in Functional Analysis291Mappings whose derivatives are isometries293Localizable functionals297Jordan maps on standard operator algebras305Pt. VIIBisymmetry and Associativity Type Equations on Quasigroups321On the functional equation S[subscript 1](x,y) = S[subscript 2](x,T(N(x),y))323Generalized associativity on rectangular quasigroups335The aggregation equation: solutions with non intersecting partial functions351
