Topics In Polynomials Of One And Several Variables And Their Applications
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Topics in Polynomials of One and Several Variables and Their Applications by Themistocles M. Rassias,H. M. Srivastava Pdf
This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications. It is dedicated to P L Chebyshev, a leading Russian mathematician.
Topics in Polynomials of One and Several Variables and Their Applications by Th M Rassias,H M Srivastava,A Yanushauskas Pdf
This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications. It is dedicated to P L Chebyshev, a leading Russian mathematician. Contents:On the Characterization of Chebyshev Systems and on Conditions of Their Extension (Y G Abakumov)On Lagrange Polynomial Quasi-Interpolation (C K Chui et al.)The Convexity of Chebyshev Sets in Hilbert Space (F Deutsch)On the Completeness of Orthogonal Polynomials in Left-Definite Sobolev Spaces (W N Everitt et al.)A New Method for Generating Infinite Sets of Related Sequences of Orthogonal Polynomials, Starting from First-Order Initial-Value Problems (C C Grosjean)Orthogonal Polynomials on n-Spheres: Gegenbauer, Jacobi and Heun (E G Kalnins & W Miller, Jr)Extremal Problems for Polynomials and Their Coefficients (G V Milovanovi et al.)Some Recent Advances in the Theory of the Zeros and Critical Points of a Polynomial (Th M Rassias & H M Srivastava)Artificial Intelligence Today (G C Rota)A Certain Family of Generating Functions for Classical Orthogonal Polynomials (H M Srivastava)Mean Number of Real Zeros of a Random Trigonometric Polynomial. II (J E Wilkins, Jr)Orthogonal Polynomials of Many Variables and Degenerated Elliptic Equations (A Yanushauskas)and other papers Readership: Mathematicians and mathematical physicists. keywords:Polynomial Inequalities;Chebyshev Polynomials;Approximation Theory;Fourier Series;Special Functions;Lagrange Polynomials;Markov, Sobolev and Bernstein Inequalities;Orthogonal Polynomials;Generating Functions;Holographic Neural Networks;Integral Equations;Integral Transforms;Rational Approximations;Elliptic Equations;Sobolev Spaces
Orthogonal Polynomials in Two Variables by P.K. Suetin Pdf
Presenting a comprehensive theory of orthogonal polynomials in two real variables and properties of Fourier series in these polynomials, this volume also gives cases of orthogonality over a region and on a contour. The text includes the classification of differential equations which admits orthogonal polynomials as eigenfunctions and several two-dimensional analogies of classical orthogonal polynomials.
Extremal Problems and Inequalities of Markov-Bernstein Type for Algebraic Polynomials by Robert B. Gardner,Narendra K. Govil,Gradimir V. Milovanovic Pdf
Bernstein-type Inequalities for Polynomials and Rational Functions is an integrated, powerful and clear presentation of the emergent field in approximation theory. It presents a unified description of solution norms relevant to complex polynomials, rational functions and exponential functions. Primarily for graduate students and first year PhDs, this book is useful for any researcher exploring problems which require derivative estimates. It is particularly useful for those studying inverse problems in approximation theory. Applies Bernstein-type Inequalities to any problem where derivative estimates are necessary Presents complex math in a clean and simple way, progressing readers from polynomials into rational functions Contains exhaustive references with thousands of citations to articles and books Features methods to solve inverse problems across approximation theory Includes open problems for further research
Recent Progress in Inequalities by G.V. Milovanovic Pdf
This volume is dedicated to the late Professor Dragoslav S. Mitrinovic(1908-1995), one of the most accomplished masters in the domain of inequalities. Inequalities are to be found everywhere and play an important and significant role in almost all subjects of mathematics as well as in other areas of sciences. Professor Mitrinovic used to say: `There are no equalities, even in human life inequalities are always encountered.' This volume provides an extensive survey of the most current topics in almost all subjects in the field of inequalities, written by 85 outstanding scientists from twenty countries. Some of the papers were presented at the International Memorial Conference dedicated to Professor D.S. Mitrinovic, which was held at the University of Nis, June 20-22, 1996. Audience: This book will be of great interest to researchers in real, complex and functional analysis, special functions, approximation theory, numerical analysis and computation, and other fields, as well as to graduate students requiring the most up-to-date results.
Survey on Classical Inequalities by Themistocles RASSIAS Pdf
Survey on Classical Inequalities provides a study of some of the well known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shannon's and related inequalities, generalized Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp -norm inequalities in convolutions, inequalities for polynomial zeros as well as applications in a number of problems of pure and applied mathematics. It is my pleasure to express my appreciation to the distinguished mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staff of Kluwer Academic Publishers. June 2000 Themistocles M. Rassias Vll LYAPUNOV INEQUALITIES AND THEIR APPLICATIONS RICHARD C. BROWN Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA. email address:[email protected] DON B. HINTON Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA. email address: [email protected] Abstract. For nearly 50 years Lyapunov inequalities have been an important tool in the study of differential equations. In this survey, building on an excellent 1991 historical survey by Cheng, we sketch some new developments in the theory of Lyapunov inequalities and present some recent disconjugacy results relating to second and higher order differential equations as well as Hamiltonian systems. 1. Introduction Lyapunov's inequality has proved useful in the study of spectral properties of ordinary differential equations. Typical applications include bounds for eigenvalues, stability criteria for periodic differential equations, and estimates for intervals of disconjugacy.
Approximation and Computation by Walter Gautschi,Giuseppe Mastroianni,Themistocles M. Rassias Pdf
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanović, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational algorithms, and multidisciplinary applications. Special features of this volume: - Presents results and approximation methods in various computational settings including: polynomial and orthogonal systems, analytic functions, and differential equations. - Provides a historical overview of approximation theory and many of its subdisciplines; - Contains new results from diverse areas of research spanning mathematics, engineering, and the computational sciences. "Approximation and Computation" is intended for mathematicians and researchers focusing on approximation theory and numerical analysis, but can also be a valuable resource to students and researchers in the computational and applied sciences.
Functional Equations and Inequalities by Themistocles RASSIAS Pdf
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, normal distributions, some difference equations, finite sums, decompositions of functions, harmonic functions, set-valued quasiconvex functions, the problems of expressibility in some extensions of free groups, Aleksandrov problem and mappings which preserve distances, Ulam's problem, stability of some functional equation for generalized trigonometric functions, Hyers-Ulam stability of Hosszú's equation, superstability of a functional equation, and some demand functions in a duopoly market with advertising. Audience: This book will be of interest to mathematicians and graduate students whose work involves real functions, functions of a complex variable, functional analysis, integral transforms, and operational calculus.
An Introduction to Hypergeometric, Supertrigonometric, and Superhyperbolic Functions by Xiao-Jun Yang Pdf
An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler Beta function, the Clausen hypergeometric series, and the Gauss hypergeometric have been successfully applied to describe the real-world phenomena that involve complex behaviors arising in mathematics, physics, chemistry, and engineering. Provides a historical overview for a family of the special polynomials Presents a logical investigation of a family of the hypergeometric series Proposes a new family of the hypergeometric supertrigonometric functions Presents a new family of the hypergeometric superhyperbolic functions
Recent Advances in Constructive Approximation Theory by Vijay Gupta,Themistocles M. Rassias,P. N. Agrawal,Ana Maria Acu Pdf
This book presents an in-depth study on advances in constructive approximation theory with recent problems on linear positive operators. State-of-the-art research in constructive approximation is treated with extensions to approximation results on linear positive operators in a post quantum and bivariate setting. Methods, techniques, and problems in approximation theory are demonstrated with applications to optimization, physics, and biology. Graduate students, research scientists and engineers working in mathematics, physics, and industry will broaden their understanding of operators essential to pure and applied mathematics. Topics discussed include: discrete operators, quantitative estimates, post-quantum calculus, integral operators, univariate Gruss-type inequalities for positive linear operators, bivariate operators of discrete and integral type, convergence of GBS operators.
