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Hahn–Banach Theorem
The notion of extension in continuity of a linear continuous functional is introduced an famous Hahn-Banach theorem is formulated, together with...
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On the Equivalence in ZF+BPI of the Hahn–Banach Theorem and Three Classical Theorems
The presented paper is a compendium or a kind of précis of relationships between the four classical theorems of mathematical analysis. More...
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Hahn-Banach Theorems
The analytic form of the Hahn-Banach theorem concerns the extension of linear functionals defined on a subspace of a normed linear space to the...
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Representation of uniform boundedness principle and Hahn–Banach theorem in linear n-normed space
The concept of b-linear functional and its different types of continuity in linear n-normed space are presented and some of their properties are...
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Uniqueness of Hahn–Banach extensions and some of its variants
In this paper, we analyze the various strengthening and weakening of the uniqueness of the Hahn–Banach extension. In addition, we consider the case...
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Introduction to Convex Analysis: The Hahn-Banach and Lax-Milgram Theorems
Before we start diving into integral functionals, it is important to devout some time to understand relevant facts for abstract variational problems....
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Order Versions of the Hahn–Banach Theorem and Envelopes. II. Applications to Function Theory
In this paper, we consider the problem on the existence of the upper (lower) envelope of a convex cone or, more generally, a convex set for functions...
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The Hahn–Banach Theorem
The Hahn–Banach theorem is another fundamental principle of functional analysis, which allows extending continuous linear functionals on a subspace...
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Metric Compactness Criteria Involving Sequences of Map**s and a Proof of the Ascoli–Arzelà Theorem with the use of Bernstein Polynomials
We establish inter alia a compactness criterion in metric spaces involving a sequence of completely continuous map**s, which is continuously...
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Banach Spaces
This chapter explores the properties of operators and functionals on general Banach spaces, with the aim of generalizing various results on Hilbert...
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Group invariant variational principles
In this paper we introduce a group invariant version of the well-known Ekeland variational principle. To achieve this, we define the concept of...
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Baire’s Theorem and Applications
Baire’s theorem is a result on complete metric spaces which will be used in this chapter to prove some very important results on Banach spaces.
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Duality and Linear Operators
The aim of this chapter is to present the duality theory and to prove the fundamental theorems of the theory of locally convex spaces in a direct...
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A Metric Fixed Point Theorem and Some of Its Applications
A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing....
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Amenability of representations and invariant Hahn–Banach theorems
Invariant Hahn–Banach theorems are proved in the context of right amenable, weakly almost periodic representations of semigroups on locally convex...
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From the Hahn–Banach extension theorem to the isotonicity of convex functions and the majorization theory
The property of isotonicity of a continuous convex function on the positive cone is characterized via subdifferentials. This is used to illustrate a...
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The Hahn–Banach theorem: a proof of the equivalence between the analytic and geometric versions
We present here a simple and direct proof of the classic geometric version of the Hahn–Banach theorem from its analytic version, in the real case....
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A Mean Value Theorem for Tangentially Convex Functions
The main result is an equality type mean value theorem for tangentially convex functions in terms of tangential subdifferentials, which generalizes...
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The Banach Fixed Point Theorem: selected topics from its hundred-year history
On June 24, 1920 Stefan Banach presented his doctoral dissertation titled O operacjach na zbiorach abstrakcyjnych i ich zastosowaniach do równañ...
