Fixed Point Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed Point Theory write by Andrzej Granas. This book was released on 2013-03-09. Fixed Point Theory available in PDF, EPUB and Kindle. The theory of Fixed Points is one of the most powerful tools of modern mathematics. This book contains a clear, detailed and well-organized presentation of the major results, together with an entertaining set of historical notes and an extensive bibliography describing further developments and applications. From the reviews: "I recommend this excellent volume on fixed point theory to anyone interested in this core subject of nonlinear analysis." --MATHEMATICAL REVIEWS
Iterative Approximation of Fixed Points
Iterative Approximation of Fixed Points - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Iterative Approximation of Fixed Points write by Vasile Berinde. This book was released on 2007-04-20. Iterative Approximation of Fixed Points available in PDF, EPUB and Kindle. 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.
The Computation of Fixed Points and Applications
The Computation of Fixed Points and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Computation of Fixed Points and Applications write by M. J. Todd. This book was released on 2013-03-09. The Computation of Fixed Points and Applications available in PDF, EPUB and Kindle. Fixed-point algorithms have diverse applications in economics, optimization, game theory and the numerical solution of boundary-value problems. Since Scarf's pioneering work [56,57] on obtaining approximate fixed points of continuous mappings, a great deal of research has been done in extending the applicability and improving the efficiency of fixed-point methods. Much of this work is available only in research papers, although Scarf's book [58] gives a remarkably clear exposition of the power of fixed-point methods. However, the algorithms described by Scarf have been super~eded by the more sophisticated restart and homotopy techniques of Merrill [~8,~9] and Eaves and Saigal [1~,16]. To understand the more efficient algorithms one must become familiar with the notions of triangulation and simplicial approxi- tion, whereas Scarf stresses the concept of primitive set. These notes are intended to introduce to a wider audience the most recent fixed-point methods and their applications. Our approach is therefore via triangu- tions. For this reason, Scarf is cited less in this manuscript than his contri- tions would otherwise warrant. We have also confined our treatment of applications to the computation of economic equilibria and the solution of optimization problems. Hansen and Koopmans [28] apply fixed-point methods to the computation of an invariant optimal capital stock in an economic growth model. Applications to game theory are discussed in Scarf [56,58], Shapley [59], and Garcia, Lemke and Luethi [24]. Allgower [1] and Jeppson [31] use fixed-point algorithms to find many solutions to boundary-value problems.
A Fixed-Point Farrago
A Fixed-Point Farrago - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Fixed-Point Farrago write by Joel H. Shapiro. This book was released on 2016-05-23. A Fixed-Point Farrago available in PDF, EPUB and Kindle. This text provides an introduction to some of the best-known fixed-point theorems, with an emphasis on their interactions with topics in analysis. The level of exposition increases gradually throughout the book, building from a basic requirement of undergraduate proficiency to graduate-level sophistication. Appendices provide an introduction to (or refresher on) some of the prerequisite material and exercises are integrated into the text, contributing to the volume’s ability to be used as a self-contained text. Readers will find the presentation especially useful for independent study or as a supplement to a graduate course in fixed-point theory. The material is split into four parts: the first introduces the Banach Contraction-Mapping Principle and the Brouwer Fixed-Point Theorem, along with a selection of interesting applications; the second focuses on Brouwer’s theorem and its application to John Nash’s work; the third applies Brouwer’s theorem to spaces of infinite dimension; and the fourth rests on the work of Markov, Kakutani, and Ryll–Nardzewski surrounding fixed points for families of affine maps.
Fixed-Point Algorithms for Inverse Problems in Science and Engineering
Fixed-Point Algorithms for Inverse Problems in Science and Engineering - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Fixed-Point Algorithms for Inverse Problems in Science and Engineering write by Heinz H. Bauschke. This book was released on 2011-05-27. Fixed-Point Algorithms for Inverse Problems in Science and Engineering available in PDF, EPUB and Kindle. "Fixed-Point Algorithms for Inverse Problems in Science and Engineering" presents some of the most recent work from top-notch researchers studying projection and other first-order fixed-point algorithms in several areas of mathematics and the applied sciences. The material presented provides a survey of the state-of-the-art theory and practice in fixed-point algorithms, identifying emerging problems driven by applications, and discussing new approaches for solving these problems. This book incorporates diverse perspectives from broad-ranging areas of research including, variational analysis, numerical linear algebra, biotechnology, materials science, computational solid-state physics, and chemistry. Topics presented include: Theory of Fixed-point algorithms: convex analysis, convex optimization, subdifferential calculus, nonsmooth analysis, proximal point methods, projection methods, resolvent and related fixed-point theoretic methods, and monotone operator theory. Numerical analysis of fixed-point algorithms: choice of step lengths, of weights, of blocks for block-iterative and parallel methods, and of relaxation parameters; regularization of ill-posed problems; numerical comparison of various methods. Areas of Applications: engineering (image and signal reconstruction and decompression problems), computer tomography and radiation treatment planning (convex feasibility problems), astronomy (adaptive optics), crystallography (molecular structure reconstruction), computational chemistry (molecular structure simulation) and other areas. Because of the variety of applications presented, this book can easily serve as a basis for new and innovated research and collaboration.
