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Functional Equations and Inequalities
This volume provides an extensive study of some of the most important topics of current interest in functional equations and inequalities. Subjects dealt with include: a Pythagorean functional equation, a functional definition of trigonometric functions, the functional equation of the square root spiral, a conditional Cauchy functional equation, an iterative functional equation, the Hille-type functional equation, the polynomial-like iterative functional equation, distribution of zeros and inequalities for zeros of algebraic polynomials, a qualitative study of Lobachevsky's complex functional equation, functional inequalities in special classes of functions, replicativity and function spaces...
Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis
No books dealing with a comprehensive illustration of the fast developing field of nonlinear analysis had been published for the mathematicians interested in this field for more than a half century until D. H. Hyers, G. Isac and Th. M. Rassias published their book, "Stability of Functional Equations in Several Variables". This book will complement the books of Hyers, Isac and Rassias and of Czerwik (Functional Equations and Inequalities in Several Variables) by presenting mainly the results applying to the Hyers-Ulam-Rassias stability. Many mathematicians have extensively investigated the subjects on the Hyers-Ulam-Rassias stability. This book covers and offers almost all classical results on the Hyers-Ulam-Rassias stability in an integrated and self-contained fashion.
Nonlinear Analysis and Variational Problems
The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.
Ulam’s Conjecture on Invariance of Measure in the Hilbert Cube
This book discusses the process by which Ulam's conjecture is proved, aptly detailing how mathematical problems may be solved by systematically combining interdisciplinary theories. It presents the state-of-the-art of various research topics and methodologies in mathematics, and mathematical analysis by presenting the latest research in emerging research areas, providing motivation for further studies. The book also explores the theory of extending the domain of local isometries by introducing a generalized span. For the reader, working knowledge of topology, linear algebra, and Hilbert space theory, is essential. The basic theories of these fields are gently and logically introduced. The...
Nonlinear Analysis
The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.
Functional Equations and Inequalities in Several Variables
This book outlines the modern theory of functional equations and inequalities in several variables. It consists of three parts. The first is devoted to additive and convex functions defined on linear spaces with semilinear topologies. In the second part, the problems of stability of functional equations in the sense of Ulam-Hyers-Rassias and in some function spaces are considered. In the last part, the functional equations in set-valued functions are dealt with ? for the first time in the mathematical literature. The book contains many fresh results concerning those problems.
Stability of Functional Equations in Several Variables
The notion of stability of functional equations of several variables in the sense used here had its origins more than half a century ago when S. Ulam posed the fundamental problem and Donald H. Hyers gave the first significant partial solution in 1941. The subject has been revised and de veloped by an increasing number of mathematicians, particularly during the last two decades. Three survey articles have been written on the subject by D. H. Hyers (1983), D. H. Hyers and Th. M. Rassias (1992), and most recently by G. L. Forti (1995). None of these works included proofs of the results which were discussed. Furthermore, it should be mentioned that wider interest in this subject area has increa...
Functional Equations, Inequalities and Applications
Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics. This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.
Mathematical Reviews
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