Ebook: Functional Equations — Results and Advances

The theory of functional equations has been developed in a rapid and productive way in the second half of the Twentieth Century. First of all, this is due to the fact that the mathematical applications raised the investigations of newer and newer types of functional equations. At the same time, the self development of this theory was also very fruitful. This can be followed in many monographs that treat and discuss the various methods and approaches. These developments were also essentially influenced by a number jour­ nals, for instance, by the Publicationes Mathematicae Debrecen (founded in 1953) and by the Aequationes Mathematicae (founded in 1968), be­ cause these journals published papers from the field of functional equa­ tions readily and frequently. The latter journal also publishes the yearly report of the International Symposia on Functional Equations and a comprehensive bibliography of the most recent papers. At the same time, there are periodically and traditionally organized conferences in Poland and in Hungary devoted to functional equations and inequali­ ties. In 2000, the 38th International Symposium on Functional Equations was organized by the Institute of Mathematics and Informatics of the University of Debrecen in Noszvaj, Hungary. The report about this meeting can be found in Aequationes Math. 61 (2001), 281-320.

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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. 

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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. 

Content:
Front Matter....Pages i-x
Front Matter....Pages 1-1
On Some Trigonometric Functional Inequalities....Pages 3-15
On the Continuity of Additive—Like Functions and Jensen Convex Functions which are Borel on a Sphere....Pages 17-20
Note on a Functional—Differential Inequality....Pages 21-24
A Characterization of Stationary Sets for the Class of Jensen Convex Functions....Pages 25-28
On the Characterization of Weierstrass’s Sigma Function....Pages 29-79
On a Mikusi?ski—Jensen Functional Equation....Pages 81-87
Front Matter....Pages 89-89
Stability of the Multiplicative Cauchy Functional Equation in Ordered Fields....Pages 91-98
On Approximately Monomial Functions....Pages 99-111
Les Op?rateurs de Hyers....Pages 113-122
Geometrical Aspects of Stability....Pages 123-132
Front Matter....Pages 133-133
On Semi-Conjugacy Equation for Homeomorphisms of the Circle....Pages 135-158
A Survey of Results and Open Problems on the Schilling Equation....Pages 159-174
Properties of an Operator Acting on the Space of Bounded Real Functions and Certain Subspaces....Pages 175-186
Front Matter....Pages 187-187
A Matkowski-Sut? Type Problem for Quasi-Arithmetic Means of Order ?....Pages 189-200
An Extension Theorem for the Matkowski—Sut? Problem for Conjugate Arithmetic Means....Pages 201-208
Homogeneous Cauchy Mean Values....Pages 209-218
On Invariant Generalized Beckenbach-Gini Means....Pages 219-230
Final Part of the Answer to a Hilbert’s Question....Pages 231-242
Front Matter....Pages 243-243
A Generalization of D’Alembert’s Functional Equation....Pages 245-248
About a Remarkable Functional Equation on some Restricted Domains....Pages 249-262
Front Matter....Pages 243-243
On Discrete Spectral Synthesis....Pages 263-274
Hyers Theorem and the Cocycle Property....Pages 275-290
Front Matter....Pages 291-291
Mappings Whose Derivatives are Isometries....Pages 293-296
Localizable Functionals....Pages 297-304
Jordan Maps on Standard Operator Algebras....Pages 305-320
Front Matter....Pages 321-321
Generalized Associativity on Rectangular Quasigroups....Pages 323-334
The Aggregation Equation: Solutions with Non Intersecting Partial Functions....Pages 335-349
Back Matter....Pages 351-360
....Pages 361-361