Fixed Points of Nonlinear Operators

Fixed Points of Nonlinear Operators PDF

Author: Haiyun Zhou

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2020-06-08

Total Pages: 377

ISBN-13: 3110667096

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Iterative Methods for Fixed Points of Nonlinear Operators offers an introduction into iterative methods of fixed points for nonexpansive mappings, pseudo-contrations in Hilbert Spaces and in Banach Spaces. Iterative methods of zeros for accretive mappings in Banach Spaces and monotone mappings in Hilbert Spaces are also discussed. It is an essential work for mathematicians and graduate students in nonlinear analysis.

Nonlinear Problems in Abstract Cones

Nonlinear Problems in Abstract Cones PDF

Author: Dajun Guo

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 286

ISBN-13: 1483261905

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Notes and Reports in Mathematics in Science and Engineering, Volume 5: Nonlinear Problems in Abstract Cones presents the investigation of nonlinear problems in abstract cones. This book uses the theory of cones coupled with the fixed point index to investigate positive fixed points of various classes of nonlinear operators. Organized into four chapters, this volume begins with an overview of the fundamental properties of cones coupled with the fixed point index. This text then employs the fixed point theory developed to discuss positive solutions of nonlinear integral equations. Other chapters consider several examples from integral and differential equations to illustrate the abstract results. This book discusses as well the fixed points of increasing and decreasing operators. The final chapter deals with the development of the theory of nonlinear differential equations in cones. This book is a valuable resource for graduate students in mathematics. Mathematicians and researchers will also find this book useful.

Convergence Theorems of Fixed Points for Classes of Nonlinear Operator

Convergence Theorems of Fixed Points for Classes of Nonlinear Operator PDF

Author: Saeed Mohammed Altwqi

Publisher: LAP Lambert Academic Publishing

Published: 2012-03-01

Total Pages: 104

ISBN-13: 9783848417919

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The main purpose of this thesis is to establish the convergence theorems of fixed points for classes of nonlinear operators in difierent types of spaces such as normed spaces, Banach spaces, uniformly convex Banach spaces, and convex metric spaces. In Chapter 1, contains some fundamental concepts. In Chapter 2, we establish approximate common fixed points of three quasi-contractive operators on a normed space through an iteration process with errors. And we show that the Noor iteration converges faster than the Ishikawa and Mann iteration for the class of Zamfirescu operators. In chapter 3, we prove the convergence theorems for nonexpansive nonself mappings. In Chapter 4, we prove some strong and weak convergence theorems for generalized three step iterative scheme to approximate common fixed points of three asymptotically nonexpansive nonself mappings. In Chapter 5 we prove the convergence of the three-step iterative scheme for three mappings of asymptotically quasi-nonexpansive type in convex metric space.

Nonlinear Functional Analysis in Banach Spaces and Banach Algebras

Nonlinear Functional Analysis in Banach Spaces and Banach Algebras PDF

Author: Aref Jeribi

Publisher: CRC Press

Published: 2015-08-14

Total Pages: 369

ISBN-13: 1498733891

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Uncover the Useful Interactions of Fixed Point Theory with Topological StructuresNonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications is the first book to tackle the topological fixed point theory for block operator matrices w

Iterative Approximation of Fixed Points

Iterative Approximation of Fixed Points PDF

Author: Vasile Berinde

Publisher: Springer

Published: 2007-04-20

Total Pages: 338

ISBN-13: 3540722343

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This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.

Fixed Point Theory and Its Applications

Fixed Point Theory and Its Applications PDF

Author: Robert F. Brown

Publisher: American Mathematical Soc.

Published: 1988

Total Pages: 280

ISBN-13: 0821850806

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Represents the proceedings of an informal three-day seminar held during the International Congress of Mathematicians in Berkeley in 1986. This work covers topics including topological fixed point theory from both the algebraic and geometric viewpoints, and the fixed point theory of nonlinear operators on normed linear spaces and its applications.

An Introduction to Nonlinear Analysis: Applications

An Introduction to Nonlinear Analysis: Applications PDF

Author: Zdzislaw Denkowski

Publisher: Springer Science & Business Media

Published: 2003-01-31

Total Pages: 844

ISBN-13: 9780306474569

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This book offers an exposition of the main applications of Nonlinear Analysis, beginning with a chapter on Nonlinear Operators and Fixed Points, a connecting point and bridge from Nonlinear Analysis theory to its applications. The topics covered include applications to ordinary and partial differential equations, optimization, optimal control, calculus of variations and mathematical economics. The presentation is supplemented with the inclusion of many exercises and their solutions.

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