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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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Continuity
In the previous chapters, we have introduced the concept of topological space, as well as a variety of concepts related to proximity. Following our...
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Continuity
In this chapter we introduce one of the most important concepts in mathematical analysis: the “continuity” of a function. This topic will be treated...
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Uniform Continuity of Multifunctions
The main objective of this article is to introduce a global version of continuity of multifunctions. Such a family of multifunctions is called...
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The Boundary Hölder Continuity of Map**s with the Poletsky Condition
We consider map**s distorting the modulus of families of paths by means of a Poletsky type inequality. At boundary points of a domain, we prove the...
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Continuity
In Chap. 9 , we have seen many examples of limits for real functions. For a function...
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Cardinality and IOD-type continuity of pullback attractors for random nonlocal equations on unbounded domains
We study the continuity set (the set of all continuous points) of pullback random attractors from a parametric space into the space of all compact...
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Convergence and Continuity
The idea of a sequence converging to a limit is defined rigorously in a general metric space. Examples are taken from real analysis, and it is shown...
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On Bolzano and Greek Concepts of Continuity
In ancient Greek, continuity referred to lines, figures, and solids, or time, place, and motion. All these objects were considered continuous in the...
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Geometry on the Finite Time Collapsing for Continuity Method
This paper is concerned about a class of finite time collapsing along continuity method over a compact Kähler manifold. It is shown that along the...
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Three point analogue of Ćirić-Reich-Rus type map**s with non-unique fixed points
In this paper, we introduce a three-point analogue of Ćirić-Reich-Rus type map**s, termed as generalized Ćirić-Reich-Rus type map**s. We...
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Continuity of the Temperature in a Multi-Phase Transition Problem. Part III
We establish local continuity of locally bounded weak solutions to a doubly nonlinear parabolic equation that models the temperature in multi-phase...
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Lipschitz-continuity of Spherically Convex Functions
In this article, some basic and important properties of spherically convex functions, such as the Lipschitz-continuity, are investigated. It is shown...
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The Moduli of Continuity for Operator Fractional Brownian Motion
The almost-sure sample path behavior of the operator fractional Brownian motion with exponent D , including multivariate fractional Brownian motion,...
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Stability of Optimal Points with Respect to Improvement Sets
The aim of this paper is to study the stability of optimal point sets based on the improvement set E by using the scalarization method and the...
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The KAM theorem on the modulus of continuity about parameters
In this paper, we study the Hamiltonian systems H ( y , x , ξ , ε ) = 〈 ω ( ξ ), y 〉+ εP ( y , x , ξ , ε ), where ω and P are continuous about ξ . We prove that...
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Continuity of Some Standard Geometric Operations
The tools from the earlier chapters are used to prove continuity and openness results for a variety of geometric constructions, including those...
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Structural Stability of the Financial Market Model: Continuity of Superhedging Price and Model Approximation
The present paper continues the topic of our recent paper in the same journal, aiming to show the role of structural stability in financial modeling....
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Limits and Continuity
The notion of limit does not only play a role for sequences, also a function f : D → W can have limits in the points a ∈ D and in the boundary...