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Bifurcation of Limit Cycles for a Perturbed Piecewise Quadratic Differential Systems
In this paper, the bifurcation of limit cycles for planar piecewise smooth systems is studied which is separated by a straight line. We give a new...
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Symmetric Strong Diameter Two Property
We study Banach spaces with the property that, given a finite number of slices of the unit ball, there exists a direction such that all these slices...
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Maps with the Radon–Nikodým Property
We study dentable maps from a closed convex subset of a Banach space into a metric space as an attempt of generalize the Radon-Nikodým property to a...
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Differentiability and Weak Differentiability
We show that although the differentiability and the weak differentiability are different “locally”, these notions coincide almost everywhere...
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Impact of the Radon–Nikodým property on convex approximation properties
A classical result states that the approximation property (AP) of a dual space X * is metric whenever X * or X ** has the Radon–Nikodým property (RNP)....
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On Lipschitz Maps, Martingales, and the Radon–Nikodým Property for \({\mathsf{F}}\)-Spaces
The development of the Radon–Nikodým property in Banach spaces sprang from the study of the differentiability of Lipschitz maps from the real line...
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Some Full Characterizations of Differentiable Functions
We give necessary and sufficient conditions for a Banach space valued function F : [0, 1] → X to be almost everywhere differentiable on [0, 1] in...
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Existence of best simultaneous approximations in L p (S,Σ,X) without the RNP assumption
Let ( S ,Σ, µ) be a complete positive σ -finite measure space and let X be a Banach space. We consider the simultaneous proximinality problem in L ...
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The Average Range Characterization of the Radon–Nikodym Property
A characterization of Banach spaces possessing the Radon—Nikodym property is given in terms of the average range of additive interval functions. We...
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A variational mcshane integral characterization of the Radon-Nikodym property
We present a new characterization of Banach spaces possessing the Radon-Nikodym property in terms of additive interval functions whose McShane...
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On Preserved and Unpreserved Extreme Points
An extreme point of the closed unit ball of a Banach space is said to be preserved if it is extreme of the closed unit ball of the bidual space;...
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The isometrical extensions of 1-Lipschitz map**s on Gâteaux differentiability spaces
Let X and Y be real Banach spaces. Suppose that the subset sm [ S 1 ( X )] of the smooth points of the unit sphere S 1 ( X ) is dense in S ...
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Sums of SCD sets and their applications to SCD operators and narrow operators
We answer two open questions concerning the recently introduced notions of slicely countably determined (SCD) sets and SCD operators in Banach...
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On geometric properties of the spaces L p(x)
We study the reflexivity, the uniform convexity, the Daugavet property and the Radon-Nikodym property of the generalized Lebesgue spaces L ...
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Fragmentability in banach spaces: Interaction of topologies
Let ( X, τ ) be a topological space and let ρ be a metric on X . Then one occasionally encounters the following situation: For each ε > 0 and a...
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On isometric extension problem between two unit spheres
In this paper we introduce the isometric extension problem of isometric map**s between two unit spheres. Some important results of the related...
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Remarks on the Cwikel–Lieb–Rozenblum and Lieb–Thirring Estimates for Schrödinger Operators on Riemannian Manifolds
Let M be a general complete Riemannian manifold and consider a Schrödinger operator −Δ+ V on L 2 ( M ). We prove Cwikel–Lieb–Rozenblum as well as...
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Asplund Spaces, Stegall Variational Principle and the RNP
Given a pair of Banach spaces X and Y such that one is the dual of the other, we study the relationships between generic Fréchet differentiability of...