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Measures Of Noncompactness And Condensing Operators

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Measures Of Noncompactness And Condensing Operators

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Author : R. R. Akhmerov
language : en
Publisher: Birkhauser
Release Date : 1992

Measures Of Noncompactness And Condensing Operators written by R. R. Akhmerov and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.

Measures Of Noncompactness And Condensing Operators

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Author : Akhmerov
language : en
Publisher: Birkhäuser
Release Date : 2014-10-05

Measures Of Noncompactness And Condensing Operators written by Akhmerov and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-05 with Science categories.

A condensing (or densifying) operator is a mapping under which the image of any set is in a certain sense more compact than the set itself. The degree of noncompactness of a set is measured by means of functions called measures of noncompactness. The contractive maps and the compact maps [i.e., in this Introduction, the maps that send any bounded set into a relatively compact one; in the main text the term "compact" will be reserved for the operators that, in addition to having this property, are continuous, i.e., in the authors' terminology, for the completely continuous operators] are condensing. For contractive maps one can take as measure of noncompactness the diameter of a set, while for compact maps can take the indicator function of a family of non-relatively com pact sets. The operators of the form F( x) = G( x, x), where G is contractive in the first argument and compact in the second, are also condensing with respect to some natural measures of noncompactness. The linear condensing operators are characterized by the fact that almost all of their spectrum is included in a disc of radius smaller than one. The examples given above show that condensing operators are a sufficiently typical phenomenon in various applications of functional analysis, for example, in the theory of differential and integral equations. As is turns out, the condensing operators have properties similar to the compact ones.

Measures Of Noncompactness And Condensing Operators

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Author : Akhmerov
language : en
Publisher: Birkhäuser
Release Date : 2013-11-21

Measures Of Noncompactness In Metric Fixed Point Theory

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Author : J.M. Ayerbe Toledano
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Measures Of Noncompactness In Metric Fixed Point Theory written by J.M. Ayerbe Toledano and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

What is clear and easy to grasp attracts us; complications deter David Hilbert The material presented in this volume is based on discussions conducted in peri odically held seminars by the Nonlinear Functional Analysis research group of the University of Seville. This book is mainly addressed to those working or aspiring to work in the field of measures of noncompactness and metric fixed point theory. Special em phasis is made on the results in metric fixed point theory which were derived from geometric coefficients defined by means of measures of noncompactness and on the relationships between nonlinear operators which are contractive for different measures. Several topics in these notes can be found either in texts on measures of noncompactness (see [AKPRSj, [BG]) or in books on metric fixed point theory (see [GK1], [Sm], [Z]). Many other topics have come from papers where the authors of this volume have published the results of their research over the last ten years. However, as in any work of this type, an effort has been made to revise many proofs and to place many others in a correct setting. Our research was made possible by partial support of the D.G.I.C.y'T. and the Junta de Andalucia.

Sequence Spaces And Measures Of Noncompactness With Applications To Differential And Integral Equations

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Author : Józef Banaś
language : en
Publisher: Springer
Release Date : 2014-07-18

Sequence Spaces And Measures Of Noncompactness With Applications To Differential And Integral Equations written by Józef Banaś and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-18 with Mathematics categories.

This book deals with the study of sequence spaces, matrix transformations, measures of noncompactness and their various applications. The notion of measure of noncompactness is one of the most useful ones available and has many applications. The book discusses some of the existence results for various types of differential and integral equations with the help of measures of noncompactness; in particular, the Hausdorff measure of noncompactness has been applied to obtain necessary and sufficient conditions for matrix operators between BK spaces to be compact operators. The book consists of eight self-contained chapters. Chapter 1 discusses the theory of FK spaces and Chapter 2 various duals of sequence spaces, which are used to characterize the matrix classes between these sequence spaces (FK and BK spaces) in Chapters 3 and 4. Chapter 5 studies the notion of a measure of noncompactness and its properties. The techniques associated with measures of noncompactness are applied to characterize the compact matrix operators in Chapters 6. In Chapters 7 and 8, some of the existence results are discussed for various types of differential and integral equations, which are obtained with the help of argumentations based on compactness conditions.

Measure Of Noncompactness Fixed Point Theorems And Applications

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Author : S. A. Mohiuddine
language : en
Publisher: CRC Press
Release Date : 2024-04-24

Measure Of Noncompactness Fixed Point Theorems And Applications written by S. A. Mohiuddine and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-24 with Mathematics categories.

The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem. Key Highlights: Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm Showcases applications of the measure of noncompactness and Petryshyn’s fixed point theorem functional integral equations in Banach algebra Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbo’s fixed point theorem Discusses best proximity point results using measure of noncompactness and its applications Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness This reference work is for scholars and academic researchers in pure and applied mathematics.

Positive Operators And Fixed Point Theorems With Applications

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Author : S. A. Mohiuddine
language : en
Publisher: Springer Nature
Release Date : 2025-05-29

Positive Operators And Fixed Point Theorems With Applications written by S. A. Mohiuddine and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-29 with Mathematics categories.

This book presents original research on the theory of positive operators, alongside fixed-point theorems and their diverse applications. It introduces various positive operators and explores their approximation properties, including Korovkin-type theorems, Voronovskaja-type results, convergence rate, and other related findings. Additionally, the book addresses the existence of solutions for various differential and integral equations in different Banach spaces by using Darbo-type fixed-point theorems. This book also presents an interplay between positive operators and fixed-point theory. Each chapter is self-contained, addressing a current problem and outlining solutions and potential applications. The chapters provide sufficient background to ensure that new definitions and results can be understood independently.

Mathematical Analysis Of Infectious Diseases

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Author : Praveen Agarwal
language : en
Publisher: Academic Press
Release Date : 2022-06-01

Mathematical Analysis Of Infectious Diseases written by Praveen Agarwal and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Science categories.

Mathematical Analysis of Infectious Diseases updates on the mathematical and epidemiological analysis of infectious diseases. Epidemic mathematical modeling and analysis is important, not only to understand disease progression, but also to provide predictions about the evolution of disease. One of the main focuses of the book is the transmission dynamics of the infectious diseases like COVID-19 and the intervention strategies. It also discusses optimal control strategies like vaccination and plasma transfusion and their potential effectiveness on infections using compartmental and mathematical models in epidemiology like SI, SIR, SICA, and SEIR. The book also covers topics like: biodynamic hypothesis and its application for the mathematical modeling of biological growth and the analysis of infectious diseases, mathematical modeling and analysis of diagnosis rate effects and prediction of viruses, data-driven graphical analysis of epidemic trends, dynamic simulation and scenario analysis of the spread of diseases, and the systematic review of the mathematical modeling of infectious disease like coronaviruses. - Offers analytical and numerical techniques for virus models - Discusses mathematical modeling and its applications in treating infectious diseases or analyzing their spreading rates - Covers the application of differential equations for analyzing disease problems - Examines probability distribution and bio-mathematical applications

Spectral Theory For Linear Operators

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Author : Bilel Krichen
language : en
Publisher: CRC Press
Release Date : 2025-08-01

Spectral Theory For Linear Operators written by Bilel Krichen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-01 with Mathematics categories.

This book focuses on spectral theory for linear operators involving bounded or unbounded demicompact linear operators acting on Banach spaces. This class played an important rule in the theory of perturbation. More precisely, it contributed in the construction of several classes of stability of essential spectra for bounded or unbounded linear operators. We should emphasize that this book is the first one dealing with the demicompactness concept and its relation with Fredholm theory for bounded and unbounded linear operators as well as block operator matrices acting on Banach spaces. Researchers, as well as graduate students in applicable analysis, will find that this book constitutes a useful survey of the fundamental principles of the subject. Nevertheless, the reader is assumed to be, at least, familiar with some related sections concerning notions like the compact, Fredholm operators, the basic tools of the weak topology, the concept of measures of weak noncompactness, etc. Otherwise, the reader is urged to consult the recommended literature in order to benefit fully from this book. Features - • First book dealing with demicompactness theory and its relation with Fredholm theory for bounded and unbounded linear operators as well as block operator matrices acting on Banach spaces. • Self-contained coverage of classical and more recent classes of perturbations involving the concept of demicompactness. • Offers a useful survey of the fundamental principles of spectral theory. • Provides applications for problem arising in physics and which are modeled by integral or partial differential equations.

Analysis Approximation Optimization Computation And Applications

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Author : Marija P. Stanić
language : en
Publisher: Springer Nature
Release Date : 2025-07-14

Analysis Approximation Optimization Computation And Applications written by Marija P. Stanić and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-14 with Mathematics categories.

This contributed volume is dedicated to Academician Gradimir V. Milovanović on his 75th birthday and contains recent results in the fields of approximation theory, numerical analysis, mathematical analysis, optimization theory, and various applications of an interdisciplinary character. Most of these results were presented in person during an International Conference “Analysis, Approximations and Applications" (AAA2023), organized by the Faculty of Science, University of Kragujevac in Vrnjačka Banja, Serbia (June 21-24, 2023). This book is intended for researchers and students of mathematics and other computational and applied sciences. This book provides surveys of state of the art results in the fields of Extremal Problems, Optimization and Calculus of Variations; Orthogonal Systems and Quadrature Formulas; Differential and Integral Equations, Integral Transforms and Operation Calculus; Analytic Number Theory and Special Functions; Real and Complex Functions, Sequences, Series, Approximations and Expansions; Functional Analysis, Operator Theory, Fixed Point Theory and Iterative Processes, as well as in Miscellaneous Applications.

Measures Of Noncompactness And Condensing Operators

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