Pseudosolution Of Linear Functional Equations

Author : Alexander S. Mechenov
Publisher : Springer Science & Business Media
Page : 245 pages
File Size : 44,9 Mb
Release : 2005-07-25
Category : Mathematics
ISBN : 9780387245065

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Pseudosolution of Linear Functional Equations by Alexander S. Mechenov Pdf

In the book there are introduced models and methods of construction of pseudo-solutions for the well-posed and ill-posed linear functional equations circumscribing models passive, active and complicated experiments. Two types of the functional equations are considered: systems of the linear algebraic equations and linear integral equations. Methods of construction of pseudos6lutions are developed in the presence of passive right-hand side errors for two types of operator errors: passive measurements and active representation errors of the operator, and all their combinations. For the determined and stochastic models of passive experiments the method of the least distances of construction of pseudosolutions is created, the maximum likelihood method of construction of pseudosolutions is applied for active experiments, and then methods for combinations of models of regression, of passive and of active experiments are created. We have constructed regularized variants of these methods for systems of the linear algebraic equations with the degenerated matrices and for linear integral equations of the first kind. In pure mathematics, the solution techniques of the functional equations with exact input data more often are studied. In applied mathematics, problem consists in construction of pseudosolutions, that is, solution of the hctional equations with perturbed input data. Such problem in many cases is incomparably more complicated. The book is devoted to a problem of construction of a pseudosolution (the problem of a parameter estimation) in the following fundamental sections of applied mathematics: confluent models passive, active and the every possible mixed experiments.

Author : Anatoliĭ Borisovich Antonevich
Publisher : Birkhauser
Page : 200 pages
File Size : 48,7 Mb
Release : 1996
Category : Mathematics
ISBN : UOM:39015040648985

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Linear Functional Equations by Anatoliĭ Borisovich Antonevich Pdf

Author : Prasanna K. Sahoo,Palaniappan Kannappan
Publisher : CRC Press
Page : 465 pages
File Size : 42,9 Mb
Release : 2011-02-08
Category : Mathematics
ISBN : 9781439841167

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Introduction to Functional Equations by Prasanna K. Sahoo,Palaniappan Kannappan Pdf

Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as p

Author : Yeol Je Cho,Themistocles M. Rassias,Reza Saadati
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 43,8 Mb
Release : 2013-08-27
Category : Mathematics
ISBN : 9781461484776

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Stability of Functional Equations in Random Normed Spaces by Yeol Je Cho,Themistocles M. Rassias,Reza Saadati Pdf

This book discusses the rapidly developing subject of mathematical analysis that deals primarily with stability of functional equations in generalized spaces. The fundamental problem in this subject was proposed by Stan M. Ulam in 1940 for approximate homomorphisms. The seminal work of Donald H. Hyers in 1941 and that of Themistocles M. Rassias in 1978 have provided a great deal of inspiration and guidance for mathematicians worldwide to investigate this extensive domain of research. The book presents a self-contained survey of recent and new results on topics including basic theory of random normed spaces and related spaces; stability theory for new function equations in random normed spaces via fixed point method, under both special and arbitrary t-norms; stability theory of well-known new functional equations in non-Archimedean random normed spaces; and applications in the class of fuzzy normed spaces. It contains valuable results on stability in random normed spaces, and is geared toward both graduate students and research mathematicians and engineers in a broad area of interdisciplinary research.

Author : Ice Risteski,Val‚ry Covachev
Publisher : World Scientific
Page : 337 pages
File Size : 45,7 Mb
Release : 2001
Category : Mathematics
ISBN : 9789812799876

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Complex Vector Functional Equations by Ice Risteski,Val‚ry Covachev Pdf

The subject of complex vector functional equations is a new area in the theory of functional equations. This monograph provides a systematic overview of the authors' recently obtained results concerning both linear and nonlinear complex vector functional equations, in all aspects of their utilization. It is intended for mathematicians, physicists and engineers who use functional equations in their investigations. Contents: Linear Complex Vector Functional Equations: General Classes of Cyclic Functional Equations; Functional Equations with Operations Between Arguments; Functional Equations with Constant Parameters; Functional Equations with Constant Coefficients; Systems of Linear Functional Equations; Nonlinear Complex Vector Functional Equations: Quadratic Functional Equations; Modified Quadratic Functional Equations; Expanded Quadratic Functional Equations; Higher Order Functional Equations; Systems of Nonlinear Functional Equations. Readership: Researchers, lecturers, senior undergraduates and graduate students dealing with functional equations.

Author : Stefan Czerwik
Publisher : World Scientific
Page : 420 pages
File Size : 42,6 Mb
Release : 2002-05-14
Category : Mathematics
ISBN : 9789814489508

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Functional Equations And Inequalities In Several Variables by Stefan Czerwik Pdf

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.

Author : John Michael Rassias,E Thandapani,K Ravi,B V Senthil Kumar
Publisher : World Scientific Publishing Company
Page : 396 pages
File Size : 53,6 Mb
Release : 2017-03-20
Category : Electronic
ISBN : 9789813147621

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Functional Equations and Inequalities by John Michael Rassias,E Thandapani,K Ravi,B V Senthil Kumar Pdf

This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations. Request Inspection Copy

Author : Genrich Belitskii,Vadim Tkachenko
Publisher : Birkhäuser
Page : 223 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880794

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One-dimensional Functional Equations by Genrich Belitskii,Vadim Tkachenko Pdf

The monograph is devoted to the study of functional equations with the transformed argument on the real line and on the unit circle. Such equations systematically arise in dynamical systems, differential equations, probabilities, singularities of smooth mappings, and other areas. The purpose of the book is to present modern methods and new results in the subject, with an emphasis on a connection between local and global solvability. The general concepts developed in the book are applicable to multidimensional functional equations. Some of the methods are presented for the first time in the monograph literature. The book is addressed to graduates and researchers interested in dynamical systems, differential equations, operator theory, or the theory of functions and their applications.

Author : Antal Járai
Publisher : Springer Science & Business Media
Page : 367 pages
File Size : 53,8 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9780387244143

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Regularity Properties of Functional Equations in Several Variables by Antal Járai Pdf

This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion. A long introduction highlights the basic ideas for beginners and several applications are also included.

Author : Donald H. Hyers,George Isac,Themistocles M. Rassias
Publisher : Boston : Birkhäuser
Page : 336 pages
File Size : 48,8 Mb
Release : 1998
Category : Mathematics
ISBN : UOM:39015043146912

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Stability of Functional Equations in Several Variables by Donald H. Hyers,George Isac,Themistocles M. Rassias Pdf

A self-contained introduction to the concept for researchers and graduate students fluent in functional analysis, algebra, and topology. Presents both the classical results and current research, and investigates such related problems as the stability of the convex functional inequality and the stability of minimum points. Other topics include approximately additive and approximately linear mappings, functions with bonded nth differences, and the stability of the quadratic functional equation. Annotation copyrighted by Book News, Inc., Portland, OR

Author : George A. Anastassiou,John Michael Rassias
Publisher : Springer Nature
Page : 746 pages
File Size : 53,7 Mb
Release : 2019-11-23
Category : Mathematics
ISBN : 9783030289508

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Frontiers in Functional Equations and Analytic Inequalities by George A. Anastassiou,John Michael Rassias Pdf

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: Hyperstability of a linear functional equation on restricted domains Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces Stabilities of Functional Equations via Fixed Point Technique Measure zero stability problem for the Drygas functional equation with complex involution Fourier Transforms and Ulam Stabilities of Linear Differential Equations Hyers–Ulam stability of a discrete diamond–alpha derivative equation Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book.

Author : Sui Sun Cheng,Wenrong Li
Publisher : World Scientific Publishing Company Incorporated
Page : 284 pages
File Size : 50,7 Mb
Release : 2008
Category : Mathematics
ISBN : 9789812793348

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Analytic Solutions of Functional Equations by Sui Sun Cheng,Wenrong Li Pdf

Author : Anatolii Antonevich
Publisher : Unknown
Page : 179 pages
File Size : 51,9 Mb
Release : 1995
Category : Electronic
ISBN : 0817629319

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Linear Functional Equations by Anatolii Antonevich Pdf

Author : KREIN
Publisher : Springer Science & Business Media
Page : 112 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468480689

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Linear Equations in Banach Spaces by KREIN Pdf

INTRODUCTION . . . . . . xiii § 1. LINEAR EQUATIONS. BASIC NOTIONS . 3 § 2. EQUATIONS WITH A CLOSED OPERATOR 6 § 3. THE ADJOINT EQUATION . . . . . . 10 § 4. THE EQUATION ADJOINT TO THE FACTORED EQUATION. 17 § 5. AN EQUATION WITH A CLOSED OPERATOR WHICH HAS A DENSE DOMAIN 18 NORMALLY SOLVABLE EQUATIONS WITH FINITE DIMENSIONAL KERNEL. 22 § 6. A PRIORI ESTIMATES .. . . . . . 24 § 7. EQUATIONS WITH FINITE DEFECT . . . 27 § 8. § 9. SOME DIFFERENT ADJOINT EQUATIONS . 30 § 10. LINEAR TRANSFORMATIONS OF EQUATIONS 33 TRANSFORMATIONS OF d-NORMAL EQUATIONS . 38 § 11. § 12. NOETHERIAN EQUATIONS. INDEX. . . . . . 42 § 13. EQUATIONS WITH OPERATORS WHICH ACT IN A SINGLE SPACE 44 § 14. FREDHOLM EQUATIONS. REGULARIZATION OF EQUATIONS 46 § 15. LINEAR CHANGES OF VARIABLE . . . . . . . . 50 § 16. STABILITY OF THE PROPERTIES OF AN EQUATION 53 OVERDETERMINED EQUATIONS 59 § 17. § 18. UNDETERMINED EQUATIONS 62 § 19. INTEGRAL EQUATIONS . . . 65 DIFFERENTIAL EQUATIONS . 80 § 20. APPENDIX. BASIC RESULTS FROM FUNCTIONAL ANALYSIS USED IN THE TEXT 95 LITERATURE CITED . . . . . . . . . . . . . . . . . . .. . . . 99 . . PRE F ACE The basic material appearing in this book represents the substance v of a special series of lectures given by the author at Voronez University in 1968/69, and, in part, at Dagestan University in 1970.

Author : Michael I. Gil'
Publisher : Springer
Page : 311 pages
File Size : 54,7 Mb
Release : 2014-10-08
Category : Mathematics
ISBN : 9789462390911

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Stability of Neutral Functional Differential Equations by Michael I. Gil' Pdf

In this monograph the author presents explicit conditions for the exponential, absolute and input-to-state stabilities including solution estimates of certain types of functional differential equations. The main methodology used is based on a combination of recent norm estimates for matrix-valued functions, comprising the generalized Bohl-Perron principle, together with its integral version and the positivity of fundamental solutions. A significant part of the book is especially devoted to the solution of the generalized Aizerman problem.