Nonlinear Integral Operators And Applications

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Nonlinear Integral Operators and Applications

Author : Carlo Bardaro
Publisher : Walter de Gruyter
ISBN 13 : 3110199270
Total Pages : 214 pages
Book Rating : 4.1/5 (11 download)

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Book Synopsis Nonlinear Integral Operators and Applications by : Carlo Bardaro

Download or read book Nonlinear Integral Operators and Applications written by Carlo Bardaro and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1903 Fredholm published his famous paper on integral equations. Since then linear integral operators have become an important tool in many areas, including the theory of Fourier series and Fourier integrals, approximation theory and summability theory, and the theory of integral and differential equations. As regards the latter, applications were soon extended beyond linear operators. In approximation theory, however, applications were limited to linear operators mainly by the fact that the notion of singularity of an integral operator was closely connected with its linearity. This book represents the first attempt at a comprehensive treatment of approximation theory by means of nonlinear integral operators in function spaces. In particular, the fundamental notions of approximate identity for kernels of nonlinear operators and a general concept of modulus of continuity are developed in order to obtain consistent approximation results. Applications to nonlinear summability, nonlinear integral equations and nonlinear sampling theory are given. In particular, the study of nonlinear sampling operators is important since the results permit the reconstruction of several classes of signals. In a wider context, the material of this book represents a starting point for new areas of research in nonlinear analysis. For this reason the text is written in a style accessible not only to researchers but to advanced students as well.

Linear and Nonlinear Integral Equations

Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
ISBN 13 : 3642214495
Total Pages : 639 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Linear and Nonlinear Integral Equations by : Abdul-Majid Wazwaz

Download or read book Linear and Nonlinear Integral Equations written by Abdul-Majid Wazwaz and published by Springer Science & Business Media. This book was released on 2011-11-24 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.

Methods in Nonlinear Integral Equations

Author : R Precup
Publisher : Springer Science & Business Media
ISBN 13 : 9401599866
Total Pages : 221 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Methods in Nonlinear Integral Equations by : R Precup

Download or read book Methods in Nonlinear Integral Equations written by R Precup and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.

Partial Integral Operators and Integro-Differential Equations

Author : Jurgen Appell
Publisher : CRC Press
ISBN 13 : 9780824703967
Total Pages : 582 pages
Book Rating : 4.7/5 (39 download)

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Book Synopsis Partial Integral Operators and Integro-Differential Equations by : Jurgen Appell

Download or read book Partial Integral Operators and Integro-Differential Equations written by Jurgen Appell and published by CRC Press. This book was released on 2000-02-29 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account of integro-differential equations of the Barbashin type and partial integral operators. It presents the basic theory of Barbashin equations in spaces of continuous or measurable functions, including existence, uniqueness, stability and perturbation results. The theory and applications of partial integral operators and linear and nonlinear equations is discussed. Topics range from abstract functional-analytic approaches to specific uses in continuum mechanics and engineering.

Nonlinear Integral Equations

Author : Philip M. Anselone
Publisher :
ISBN 13 :
Total Pages : 400 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Nonlinear Integral Equations by : Philip M. Anselone

Download or read book Nonlinear Integral Equations written by Philip M. Anselone and published by . This book was released on 1964 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Singular Integral Equations

Author : E.G. Ladopoulos
Publisher : Springer Science & Business Media
ISBN 13 : 3662042916
Total Pages : 569 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Singular Integral Equations by : E.G. Ladopoulos

Download or read book Singular Integral Equations written by E.G. Ladopoulos and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

Author : Hemen Dutta
Publisher : Springer Nature
ISBN 13 : 3030152421
Total Pages : 912 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Current Trends in Mathematical Analysis and Its Interdisciplinary Applications by : Hemen Dutta

Download or read book Current Trends in Mathematical Analysis and Its Interdisciplinary Applications written by Hemen Dutta and published by Springer Nature. This book was released on 2019-08-23 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. Each of the 23 carefully reviewed chapters was written by experienced expert(s) in respective field, and will enrich readers’ understanding of the respective research problems, providing them with sufficient background to understand the theories, methods and applications discussed. The book’s main goal is to highlight the latest trends and advances, equipping interested readers to pursue further research of their own. Given its scope, the book will especially benefit graduate and PhD students, researchers in the applied sciences, educators, and engineers with an interest in recent developments in the interdisciplinary applications of mathematical analysis.

Nonlinear Functional Analysis and Applications

Author : Louis B. Rall
Publisher : Elsevier
ISBN 13 : 1483272443
Total Pages : 595 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Nonlinear Functional Analysis and Applications by : Louis B. Rall

Download or read book Nonlinear Functional Analysis and Applications written by Louis B. Rall and published by Elsevier. This book was released on 2014-05-10 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Functional Analysis and Applications provides information pertinent to the fundamental aspects of nonlinear functional analysis and its application. This book provides an introduction to the basic concepts and techniques of this field. Organized into nine chapters, this book begins with an overview of the possibilities for applying ideas from functional analysis to problems in analysis. This text then provides a systematic exposition of several aspects of differential calculus in norms and topological linear spaces. Other chapters consider the various settings in nonlinear functional analysis in which differentials play a significant role. This book discusses as well the generalized inverse for a bounded linear operator, whose range is not necessarily closed. The final chapter deals with the equations of hydrodynamics, which are usually highly nonlinear and difficult to solve. This book is a valuable resource for mathematicians. Readers who are interested in nonlinear functional analysis will also find this book useful.

Differential and Integral Operators

Author : Israel C. Gohberg
Publisher : Birkhäuser
ISBN 13 : 3034887892
Total Pages : 333 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Differential and Integral Operators by : Israel C. Gohberg

Download or read book Differential and Integral Operators written by Israel C. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This and the next volume of the OT series contain the proceedings of the Work shop on Operator Theory and its Applications, IWOTA 95, which was held at the University of Regensburg, Germany, July 31 to August 4, 1995. It was the eigth workshop of this kind. Following is a list of the seven previous workshops with reference to their proceedings: 1981 Operator Theory (Santa Monica, California, USA) 1983 Applications of Linear Operator Theory to Systems and Networks (Rehovot, Israel), OT 12 1985 Operator Theory and its Applications (Amsterdam, The Netherlands), OT 19 1987 Operator Theory and Functional Analysis (Mesa, Arizona, USA), OT 35 1989 Matrix and Operator Theory (Rotterdam, The Netherlands), OT 50 1991 Operator Theory and Complex Analysis (Sapporo, Japan), OT 59 1993 Operator Theory and Boundary Eigenvalue Problems (Vienna, Austria), OT 80 IWOTA 95 offered a rich programme on a wide range of latest developments in operator theory and its applications. The programme consisted of 6 invited plenary lectures, 54 invited special topic lectures and more than 100 invited session talks. About 180 participants from 25 countries attended the workshop, more than a third came from Eastern Europe. The conference covered different aspects of linear and nonlinear spectral prob lems, starting with problems for abstract operators up to spectral theory of ordi nary and partial differential operators, pseudodifferential operators, and integral operators. The workshop was also focussed on operator theory in spaces with indefinite metric, operator functions, interpolation and extension problems.

Nonlinear Integral Equations and Inclusions

Author : Ravi P. Agarwal
Publisher : Nova Publishers
ISBN 13 : 9781590330944
Total Pages : 376 pages
Book Rating : 4.3/5 (39 download)

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Book Synopsis Nonlinear Integral Equations and Inclusions by : Ravi P. Agarwal

Download or read book Nonlinear Integral Equations and Inclusions written by Ravi P. Agarwal and published by Nova Publishers. This book was released on 2001 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Integral Equations

Author : Harry Hochstadt
Publisher : John Wiley & Sons
ISBN 13 : 1118165934
Total Pages : 282 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis Integral Equations by : Harry Hochstadt

Download or read book Integral Equations written by Harry Hochstadt and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work is now available in an unabridged paperback edition. Hochstatdt's concise treatment of integral equations represents the best compromise between the detailed classical approach and the faster functional analytic approach, while developing the most desirable features of each. The seven chapters present an introduction to integral equations, elementary techniques, the theory of compact operators, applications to boundary value problems in more than dimension, a complete treatment of numerous transform techniques, a development of the classical Fredholm technique, and application of the Schauder fixed point theorem to nonlinear equations.

Theory and Applications of Nonlinear Operators of Accretive and Monotone Type

Author : Athanass Kartsatos
Publisher : CRC Press
ISBN 13 : 9780824797218
Total Pages : 338 pages
Book Rating : 4.7/5 (972 download)

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Book Synopsis Theory and Applications of Nonlinear Operators of Accretive and Monotone Type by : Athanass Kartsatos

Download or read book Theory and Applications of Nonlinear Operators of Accretive and Monotone Type written by Athanass Kartsatos and published by CRC Press. This book was released on 1996-03-14 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is based upon a Special Session on the Theory and Applications of Nonlinear Operators of Accretive and Monotone Type held during the recent meeting of the American Mathematical Society in San Francisco. It examines current developments in non-linear analysis, emphasizing accretive and monotone operator theory. The book presents a major survey/research article on partial functional differential equations with delay and an important survey/research article on approximation solvability.

Abel Integral Equations

Author : Rudolf Gorenflo
Publisher : Springer
ISBN 13 : 3540469494
Total Pages : 225 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Abel Integral Equations by : Rudolf Gorenflo

Download or read book Abel Integral Equations written by Rudolf Gorenflo and published by Springer. This book was released on 2006-11-14 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.

Mathematical Modelling, Applied Analysis and Computation

Author : Jagdev Singh
Publisher : Springer Nature
ISBN 13 : 9811396086
Total Pages : 311 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Mathematical Modelling, Applied Analysis and Computation by : Jagdev Singh

Download or read book Mathematical Modelling, Applied Analysis and Computation written by Jagdev Singh and published by Springer Nature. This book was released on 2019-08-31 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains original research papers presented at the International Conference on Mathematical Modelling, Applied Analysis and Computation, held at JECRC University, Jaipur, India, on 6-8 July, 2018. Organized into 20 chapters, the book focuses on theoretical and applied aspects of various types of mathematical modelling such as equations of various types, fuzzy mathematical models, automata, Petri nets and bond graphs for systems of dynamic nature and the usage of numerical techniques in handling modern problems of science, engineering and finance. It covers the applications of mathematical modelling in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science and finance. A wide variety of dynamical systems like deterministic, stochastic, continuous, discrete or hybrid, with respect to time, are discussed in the book. It provides the mathematical modelling of various problems arising in science and engineering, and also new efficient numerical approaches for solving linear and nonlinear problems and rigorous mathematical theories, which can be used to analyze a different kind of mathematical models. The conference was aimed at fostering cooperation among students and researchers in areas of applied analysis, engineering and computation with the deliberations to inculcate new research ideas in their relevant fields. This volume will provide a comprehensive introduction to recent theories and applications of mathematical modelling and numerical simulation, which will be a valuable resource for graduate students and researchers of mathematical modelling and industrial mathematics.

Bounded and Compact Integral Operators

Author : David E. Edmunds
Publisher : Springer Science & Business Media
ISBN 13 : 940159922X
Total Pages : 655 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Bounded and Compact Integral Operators by : David E. Edmunds

Download or read book Bounded and Compact Integral Operators written by David E. Edmunds and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness).

Integral Operators in Non-Standard Function Spaces

Author : Vakhtang Kokilashvili
Publisher : Birkhäuser
ISBN 13 : 3319210157
Total Pages : 567 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Integral Operators in Non-Standard Function Spaces by : Vakhtang Kokilashvili

Download or read book Integral Operators in Non-Standard Function Spaces written by Vakhtang Kokilashvili and published by Birkhäuser. This book was released on 2016-05-11 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.

Nonlinear Integrals and Their Applications in Data Mining

Author : Zhenyuan Wang
Publisher : World Scientific
ISBN 13 : 9812814671
Total Pages : 359 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Nonlinear Integrals and Their Applications in Data Mining by : Zhenyuan Wang

Download or read book Nonlinear Integrals and Their Applications in Data Mining written by Zhenyuan Wang and published by World Scientific. This book was released on 2010 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regarding the set of all feature attributes in a given database as the universal set, this monograph discusses various nonadditive set functions that describe the interaction among the contributions from feature attributes towards a considered target attribute. Then, the relevant nonlinear integrals are investigated. These integrals can be applied as aggregation tools in information fusion and data mining, such as synthetic evaluation, nonlinear multiregressions, and nonlinear classifications. Some methods of fuzzification are also introduced for nonlinear integrals such that fuzzy data can be treated and fuzzy information is retrievable. The book is suitable as a text for graduate courses in mathematics, computer science, and information science. It is also useful to researchers in the relevant area.