Functional Equations and Inequalities in Several Variables by Stefan Czerwik
Functional equations have substantially grown to become an important branch of mathematics, particularly during the last two decades, with its special methods, a number of interesting results and several applications. Many aspects of functional equations containing several variables may be found by the reader in the books of J. Aczel and J. Dhombres [1], M. Kuczma [123] and D. H. Hyers, G. Isac and Th. M. Rassias [97]. For more information about the history of functional equations the reader may consult Aczel [2] and Dhombres [43].
This book combines the classical theory and examples as well as recentmost results in the subject. The recent book consists of three parts. The first one is devoted to additive functions and convex functions defined on linear spaces endowed with so-called semilinear topologies. Basic results concerning important functional equations are also included in the first part. In the second part of this book we study the problem of stability of functional equations of several variables is considered. This problem has originally been posed by S. Ulam in 1940. In 1941 D. H. Hyers gave a significant partial solution to this problem in his paper [100]. In 1978, Th. M. Rassias [178] generalized the Hyers’ result, a fact which rekindled interest in the field. Since then a number of articles have appeared in the literature. Such type of stability is now called the Ulam-Hyers-Rassias stability of functional equations.
