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Quasi-Metric Properties of the Dual Cone of an Asymmetric Normed Space
We obtain some quasi-metric properties of the dual cone of an asymmetric normed space. Thus, we prove that it is balanced, and hence its topology is...
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Asymmetric Normed Baire Space
We prove that an asymmetric normed space is never a Baire space if the topology induced by the asymmetric norm is not equivalent to the topology of a...
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Complete sets in normed linear spaces
A bounded subset of a (finite or infinite dimensional) normed linear space is said to be complete (or diametrically complete) if it cannot be...
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On duality for fuzzy quasi-normed space
Since the notion of a fuzzy quasi-normed space has important applications in constructing suitable mathematical models in theoretical computer...
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Kuhn–Tucker Type Theorems in Cone and Linear Normed Spaces
AbstractTheorems of Kuhn–Tucker type are considered in semilinear spaces, and also in linear normed spaces for, generally speaking, nonconvex sets.
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The separation of convex sets and the Krein–Milman theorem in fuzzy quasi-normed space
Motivated by some deep problems in optimization and control theory, convexity theory has been extended to the various infinite dimensional functional...
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Some Classical Problems of Geometric Approximation Theory in Asymmetric Spaces
AbstractWe establish a number of theorems of geometric approximation theory in asymmetrically normed spaces. Sets with continuous selection of the...
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Differentiating Again: Linearization in Normed Spaces
This chapter is devoted to an overview of basic linear analysis in normed spaces.
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Suns, Moons, and \(\mathring{B}\)-complete Sets in Asymmetric Spaces
Classical concepts and problems of geometric approximation theory are considered in normed and asymmetric spaces. Relations between strict suns, sets...
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Density of the Points of Continuity of the Metric Function and Projection in Asymmetric Spaces
AbstractQuestions concerning the density of the sets of points of continuity of metric functions and metric projection onto sets in asymmetric...
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Fine error bounds for approximate asymmetric saddle point problems
The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle point formulation is well...
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Continuity of a Metric Function and Projection in Asymmetric Spaces
AbstractThe article studies the continuity of left metric functions and the upper semicontinuity of left metric projections onto boundedly...
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Ball-Complete Sets and Solar Properties of Sets in Asymmetric Spaces
Several important classical concepts and problems of geometric approximation theory are extended to asymmetric spaces. We introduce the concept of
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\( \overset{\circ}{B} \)-Complete Sets: Approximative and Structural Properties
We address the approximative and structural properties of approximating sets in asymmetric spaces. More precisely, we study the...
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Finsler Manifolds
In this chapter, we begin with Minkowski normed spaces which appear as tangent spaces of Finsler manifolds, and recall Euler’s homogeneous function...
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Uniform Convexity in Nonsymmetric Spaces
AbstractUniformly convex asymmetric spaces are defined. It is proved that every nonempty closed convex set in a uniformly convex complete...
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Minkowski Geometry—Some Concepts and Recent Developments
The geometry of finite-dimensional normed spaces (= Minkowski geometry) is a research topic which is related to many other fields, such as convex...