Fractal Dimensions and Dynamical Systems

Xenofon S. Motsenigos, University of Warwick, Coventry, UK

February 2001, ISBN 1-57485-052-0, pp. 115, hardcover, US$65

One of the problems of interest in Dynamical Systems is the determination of the asymptotic behaviour of orbits. Often, we are required to find ways to describe various complicated sets (like attractors or basins of attraction for example) that are strongly related to this asymptotic behaviour problem. The aim of this book is to introduce fractal dimensions (Box-counting and Hausdorff dimensions in particular) as a tool which aids in the description and understanding of these complicated sets and, therefore, of the related dynamics.

Hyers-Ulam-Rassias Stability of Functional Equations in
Mathematical Analysis

SOON-MO JUNG, College of Science and Technology, Hong-Ik University, Korea

Monograph in Mathematics
February 2001, ISBN 1-57485-051-2, pp. 260, hardcover, US $ 85

The study of stability problems for various functional equations originated from a famous talk given by Stanislaw M. Ulam in 1940. In the talk, Ulam discussed a number of important unsolved mathematical problems. One of them was a question concerning the stability of homomorphisms. In the following year, 1941, Donald H. Hyers gave a partial solution to Ulam's question. This was the first signifant breakthrough in this area. After D. H. Hyers gave an affirmative answer to Ulam's question, a large number of papers have been published in connection with various generalizations of Ulam's problem and Hyer's theorem. In particular, Themistocles M. Rassias succeeded in extending the result of Hyer's theorem by weakening the condition for the Cauchy difference. This remarkable result of Rassias directed the concern of mathematicians towards the study of stability problems of functional equations. Unfortunately, there were no books that gave a comprehensive illustration of the fast developing field of nonlinear analysis to the mathematicians who were 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." The present book will complement the book of Hyers, Isac and Rassias by presenting mainly the results concerning the Hyers-Ulam-Rassias stability. The concept of the Hyers-Ulam-Rassias stability is a generalization of the Hyers-Ulam stability of functional equations. The subjects on the Hyers-Ulam-Rassias stability have been extensively investigated by many mathematicians. This book covers almost all classical results on the Hyers-Ulam-Rassias stability in an integrated and self-contained fashion.

Nonlinear Analysis in Geometry and Topology

Edited by THEMISTOCLES M. RASSIAS, National Technical University of Athens, Greece

Collection of original refereed papers

August 2000, ISBN 1-57485-048-2, pp. 295, hardcover, US$85

Nonlinear Analysis in Geometry and Topology is devoted to recent progress in nonlinear analysis and its applications to the solution of problems in geometry and topology. Some of the topics dealt with in this volume include: convexity and metric fixed point theory, multiple solutions of nonlinear equations via Nielsen fixed point theory, solvability of quasi variational inclusions, boundary properties for two-dimensional semiflows, nonlinear planar sprays, nonlinear Hodge structures in vector bundles, Mobius transformations of the ball, applications of non-Euclidean nonlinear methods, second order differential equations on total spaces of fiber bundles with connections, super Darboux-Egoroff equations and solutions, and finite-dimensional reductions of smooth functionals.

Mathematical Analysis and Applications

Edited by THEMISTOCLES M. RASSIAS, National Technical University of Athens, Greece

Collection of original refereed papers

June 2000, ISBN 1-57485-045-8, pp. 380, hardcover, US$89

This volume presents works devoted to recent progress in both linear and nonlinear analysis in the context of approximation theory, partial differential equations, topological analysis, function theory and a variety of applications. Some of the topics dealt with include: New results and open problems on the theory of functions with minimal critical set, Marcinkiewicz inequalities, maximum modulus of polynomials, variational inequalities, generalizations of Ky Fan minimax inequality, hypergeometric series, operational techniques and their applications in analytic and univalent function theory, non linear boundary value problems, a higher order neutral difference equation, vector analogues of Sturm-Liouville operators, on a generalized Sobolev space, gyrovector spaces in the service of hyperbolic geometry, applications of Cartanšs method, a topological generalization of the theorems of Gale-Nikaido and Mas Colell.

Complex Analysis in Several Variables

Edited by Themistocles M. Rassias, National Technical University of Athens, Greece

Collection of original refereed papers

Dec. 1988, ISBN 1-57485-43-1, pp. 200, US$65.

In this volume we present articles devoted to recent progress in both linear and nonlinear analysis in the context of approximation theory, partial differential equations, topological analysis, function theory and a variety of applications. functions with minimal critical set, Marcinkiewicz inequalities on maximum modulus of polynomials, variational inequalities, generalizations of Ky Fan minimax inequality, hypergeometric series, operational techniques and their applications in analytic and univalent function theory, non linear boundary value problems, a higher order neutral difference equation, vector analogues of Sturm-Liouville operators, on a generalized Sobolev space, gyrovector spaces in the service of hyperbolic geometry, applications of Cartans method, a topological generalization of the theorems of Gale-Nikaido and Mas Colell.

Interactions, Strings and Isotopies in Higher Order Anisotropic Superspaces

SERGIU ION VACARU, Academy of Sciences of Moldova, Republic of Moldova and
The Institute for Basic Research, U.S.A.

Dec. 1998, ISBN 1-57485-032-6, pp. 450, US$85

This is the first monograph on the geometry of locally anisotropic physics. The main subjects are the theory of field interactions, strings and diffusion processes on spaces, superspaces and isospaces with higher order anisotropy and inhomogeneity. The approach proceeds by developing the concept of higher order anisotropic (super)space which unify the logical and mathematical aspects of modern Kaluza-Klein theories and generalized Lagrange and Finsler geometry and leads to modelling of physical processes on higher order fiber (super) bundles provided with nonlinear and distinguished connections and metric structures. The view adopted is that a general field theory should incorporate all possible anisotropic and stochastic manifestations of classical and quantum interactions, and, in consequence, a corresponding modification of basic principles and mathematical methods in formulation of physical theories. This book can be also considered as a pedagogical survey on the mentioned subjects.

THE GEOMETRY OF HIGHER - ORDER FINSLER SPACES

RADU MIRON , Univ. Al.I.Cuza Iasi, Romania;
Romanian Academy of Sciences and
The Institute for Basic Research, Italy and U.S.A.

1998, ISBN 1-57485-033-4, pp. 230, US$65

The Miron's monograph is devoted to the geometry of higher-order Finsler spaces F(k)n. Whole of his theory is based on the fundamental ideas from the higher order Lagrangian dynamics. Therefore in this book are studied: Variational problems for the Lagrangians of higher order, Lagrange equations, Noether theorems, Jacobi-Ostrogradski momenta,Hamilton-Jacobi equations, higfher order energies, laws of conservation, canonical k-spray, nonlinear connection, linear connections and them structure equations, the geometrical model of a higher order Finsler space and a theory of subspaces. Here appear, for the firat time a correct definition of the notion of higher order Finsler space and a systematical study of its geometry. Also, is given the solution of the famous problem of prolongation of Riemann spaces to the jet bundle of higher order and the same problem for the prolongation of the Finsler spaces. In this way one obtains the most interesting examples of higher order Finsler spaces, extremlly useful in the construction of geometrical models for theoretical physics, higher order analytical mechanics, engineering, biology etc.

Approximation Theory and Applications

Edited by Themistocles M. Rassias, National Technical University
of Athens, Athens, Greece

Collection of original refereed papers

Dec. 1998, ISBN 1-57485-041-5, pages 200, US$65

In this volume we present articles involving theory and applications of approximations in a variety of contexts. Some of the topics dealt with include: exact inequalities for norms of intermediate derivatives of half-integer order and some of their applications, asymptotic approximation by entire functions with positive coefficients, bounds for orthogonal polynomials and other families of special functions, spline interpolation via matrix factorization , optimal oscillation points for polynomials of restricted growth on the real line, special Lagrange and Hermite interpolation processes, analytic continuation of the generalized hypergeometric series near unit argument with emphasis on the zero- balanced series,on a class of analytic functions with negative coefficients for operator on Hilbert space, Hyers-Ulam-Rassias stability of functional equations in approximation theory, a new abstract approximation theorem, as well as best approximation and coincidence theorems in topological spaces.

Nonlinear Mathematical Analysis and Applications

Edited by Themistocles M. Rassias, National Technical University of Athens, Greece

Dec. 1998, ISBN 1-57485-044-X, pages 320, US $ 70

Nonlinear Mathematical Analysis and Applications is devoted to recent advances in pure and applied analysis in the context of nonlinear partial differential equations, special aspects of nonlinear functional analys approximation theory, inequalities and topics in mathematical physics. Subjects dealt with in this volume include : nonlinear transforms and analyticity of functions, some classes of multilinear and multilateral generating functions, optimality conditions for approximation problems, some multi-dimensional integral inequalities, variational inequalities, iterative methods for nonlinear problems, fixed point theory, monotone sequences, generalized topological characteristics of nonlinear Fredholm and monotone maps and solvability of operator inclusions, minimal surfaces, approximation and numerical solution for nonlinear free boundary problems, the local conservation laws basis for one-dimensional gas dynamics, Hamiltonian symmetries, Euler-Darboux equation, asymptotic of viscoelastic model solution when viscous coefficient tends to zero, as well as existence theorems in Nelsonšs stochastic mechanics on Riemannian manifolds and space-times of general relativity.

New Frontiers in Hyperstructures
Edited by T. VOUGIOUKLlS (Democritos Univ., Trace, Greece.
and IRB, Monteroduni, Italy)