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Metric Spaces Of Non Positive Curvature

Introduction.- Fixed Point Theory in Metric Spaces: An Introduction.- Modular Function Spaces.- Geometry of Modular Function Spaces.- Fixed Point Existence Theorems in Modular Function Spaces.- Fixed Point Construction Processes.- Semigroups of Nonlinear Mappings in Modular Function Spaces.- Modular Metric Spaces.

Fixed Point Theory in Modular Function Spaces

Fixed point theorems for asymptotically nonexpansive mappings

In this paper, the authors discuss some basic properties of Morrey type Besov–Triebel spaces. The authors also give the boundedness of some operators which including pseudo-differential operators of the Hormander class Φ . (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Some properties of Morrey type Besov–Triebel spaces

This chapter gives an introduction to the theory of normed linear spaces. A skeptical reader may wonder why this topic in pure mathematics is useful in applied mathematics. The reason is quite simple: Many problems of applied mathematics can be formulated as a search for a certain function, such as the function that solves a given differential equation. Usually the function sought must belong to a definite family of acceptable functions that share some useful properties. For example, perhaps it must possess two continuous derivatives. The families that arise naturally in formulating problems are often linear spaces. This means that any linear combination of functions in the family will be another member of the family. It is common, in addition, that there is an appropriate means of measuring the “distance” between two functions in the family. This concept comes into play when the exact solution to a problem is inaccessible, while approximate solutions can be computed. We often measure how far apart the exact and approximate solutions are by using a norm. In this process we are led to a normed linear space, presumably one appropriate to the problem at hand. Some normed linear spaces occur over and over again in applied mathematics, and these, at least, should be familiar to the practitioner. Examples are the space of continuous functions on a given domain and the space of functions whose squares have a finite integral on a given domain.

Normed Linear Spaces

A unified account of the major new developments inspired by Maurey's application of Banach space ultra-products to the fixed point theory for non-expansive mappings is given in this text. The first third of the book is devoted to laying a foundation for the actual fixed point theoretic results which follow. Set theoretic and Banach space ultra-products constructions are studied in detail in the second part of the book, while the remainder of the book gives an introduction to the classical fixed point theory in addition to a discussion of normal structure.

Nonstandard Methods in Fixed Point Theory

Let X be a Banach space and μ a positive measure. In this article, we show that . Also, we investigate the positivity of the numerical index of lp -spaces.

On the numerical index of vector-valued function spaces

In this paper, we show that nonempty closed convex subsets of a metric tree enjoy many properties shared by convex subsets of Hilbert spaces and admissible subsets of hyperconvex spaces. Furthermore, we prove that a set-valued mapping T* of a metric tree M with convex values has a selection T: M → M for which d(T(x),T(y)) < d H (T*(x),T*(y)) for each x,y ∈ M. Here by d H we mean the Hausdroff distance. Many applications of this result are given.

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A Selection Theorem in Metric Trees

Department of MathematicsWashington University in St. LouisSt. Louis, MO 63130.bmaurizi@math.wustl.eduOctober 22, 2005AbstractIn this paper we examine the relationship between hyperconvex hulls and metric trees. Afterproviding a linking construction for hyperconvex spaces, we show that the four-point propertyis inherited by the hyperconvex hull, which leads to the theorem that every complete metrictree is hyperconvex. We also consider some extension theorems for these spaces.

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Metric Trees, Hyperconvex Hulls and Extensions

(2002). Mixed Partial Derivatives and Fubini's Theorem. The College Mathematics Journal: Vol. 33, No. 2, pp. 126-130.

/pdf/mixed-partial-derivatives-and-fubini-s-theorem-4f8uv62cdj.pdf

Asuman Güven Aksoy

Papers

Nonstandard Methods in Fixed Point Theory

On the numerical index of vector-valued function spaces

A Selection Theorem in Metric Trees

Metric Trees, Hyperconvex Hulls and Extensions

Mixed Partial Derivatives and Fubini's Theorem