Fixed Point Theory: Banach, Brouwer and Schauder Theorems - Shamash, Ellis
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The primary focus of this work is the Brouwer and Schauder fixed point (points that are mapped onto itself) theorems. These theroems give the existence for the presence of fixed points in normed linear spaces. Brouwer considers finite- dimensional spaces while Schauder extend the theory to infinite-dimensional spaces. For completeness we also include material on the Banach fixed point theorem. Banach¿s theorem restricts the subject of fixed points to certain mappings (contraction mapping). With these restrictions we can state sufficient conditions for the existence and uniqueness of a fixed…mehr

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Produktbeschreibung
The primary focus of this work is the Brouwer and Schauder fixed point (points that are mapped onto itself) theorems. These theroems give the existence for the presence of fixed points in normed linear spaces. Brouwer considers finite- dimensional spaces while Schauder extend the theory to infinite-dimensional spaces. For completeness we also include material on the Banach fixed point theorem. Banach¿s theorem restricts the subject of fixed points to certain mappings (contraction mapping). With these restrictions we can state sufficient conditions for the existence and uniqueness of a fixed point. Banach¿s result also provide an interative procedure for obtaining approximations for the fixed point as well as error bounds on the approximation. After providing the background material needed in the understanding of these theorems we state and provide proofs of these theorems. For each of these theorems a number of applications are considered.
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Autorenporträt
Dr. Ellis Shamash was born in Mumbia, India and received most of his primary education in Yangon, Burma. He immigrated to the USA in 1959, where he earned a PhD in engineering from the University of California (UCLA) in 1973. He also earned a Masters degree in Applied Mathematics from California State University (CSUN) in 2000.