The aim of this volume, Functional Equations and Ulam’s Problem, is to publish a well-balanced collection of works devoted to the domain of functional equations with emphasis on stability results associated with Ulam’s problem for approximate homomorphisms. This area has been a source of active and vibrant research for more than five decades. Efforts have been made for the book to constitute a valuable reference for graduate students and advanced research scientists who wish to be introduced to the state-of-the art knowledge on the problems treated, as well as to obtain an overview of important results on stability theory, from classical to the most recent.
The contributions in this collection investigate the following topics: functional equations on a semigroup, generalized Euler-Lagrange cubic functional equations, Ulam stability results for the Davison functional equation, Hyers-Ulam stability of a pexiderized functional equation, Ulam-Hyers stability in normed spaces, Hyers-Ulam stabilities for weighted operators, stability conditions for linear functional-differential equations, semilinear functional differential equations, general bi-Jensen functional equation, norm inequalities for the Chebyshev functional in Hilbert spaces, orthogonality and generalized additive mappings in Banach modules, permuting triderivations and permuting trihomomorphisms in complex Banach algebras, bi-quadratic derivations and bi-quadratic homomorphisms in Banach algebras, novel representations of mappings, linear and affine sets and relations, and solvability relations in groupoids.
A system of cosine sine functional equations on a semigroup generated by
its squares.- Orthogonality and generalized additive mappings in Banach
modules.- General system of the generalized Euler Lagrange cubic functional
equations and stability results.- Bi hom ders in Banach algebras.- Several
New Inner Product and Norm Inequalities for the Cebysev Functional in Hilbert
Spaces.- Ulam Stability results for the Davison functional equation in 2
Banach spaces.- Ulam Stability results for the Davison functional equation in
2 Banach spaces.- Delay-Dependent Stability Conditions for Semilinear
Functional Differential Equations in a Banach Space.- General Bi Jensen
Equation and C Ternary Bi Hom Derivations on C Ternary Banach Algebras.-
Hyers Ulam Stability of a Pexiderized Functional Equation.- Impact of fixed
point theory on Ulam Hyers stability in normed spaces.- The Boundedness and
HU Stabilities for Some Weighted Operators.- Permuting triderivations and
permuting trihomomorphisms in complex Banach algebras.- C bi ternary
derivations in C algebra ternary algebras.- Lie bracket
derivation-derivations in Banach algebras.- Bi quadratic derivations and bi
quadratic homomorphisms in Banach algebras.- Representation of mapping as a
sum of mappings with familiar properties.- On Ulam stability and
hyperstability of functional equations in Banach spaces and 2 Banach spaces.-
Linear and Affine Sets and Relations.- Solvability relations in groupoids.
Themistocles M. Rassias is professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional analysis, functional equations, inequalities and their applications. Professor Rassias received his PhD in mathematics from the University of California, Berkeley in 1976; his thesis advisor was Stephen Smale and his academic advisor was Shiing-Shen Chern. In addition to his extensive list of journal publications, professor Rassias has published as author or volume editor several books published with Springer. Th. M. Rassias has received several awards and is an active editorial board member of an array of journals in mathematical analysis and optimization.
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