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On the Estimation of a Convex Set
The Annals of Statistics, 1984 Given independent observations $x_1, \cdots, x_n$ drawn uniformly from an unknown compact convex set $D$ in $\mathbb{R}^p$ ($p$ known) it is desired to estimate $D$ from the observations. This problem was first considered, for $p = 2$, by Ripley and Rasson (1977). We consider a decision-theoretic approach where the loss function is $L(D, \hat{D}) = m(D
M. Moore
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The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities [PDF]
, 1955 T. W. Anderson
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Polynomially convex sets [PDF]
Bulletin of the American Mathematical Society, 1962 Gabriel Stolzenberg
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Convex and Concave Hypersoft Sets with Some Properties [PDF]
Neutrosophic Sets and Systems, 2020 . Convexity plays an imperative role in optimization, pattern classification and recognition, image processing and many other relating topics in different fields of mathematical sciences like operation research, numerical analysis etc.
Atiqe Ur Rahman +2 more
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On weakly 1-convex sets in the plane
Pracì Mìžnarodnogo Geometričnogo Centru, 2023 The present work considers the properties of generally convex sets in the plane known as weakly 1-convex. An open set is called weakly 1-convex if for any boundary point of the set there exists a straight line passing through this point and not ...
Тетяна Осіпчук +1 more
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A theoretical context for (θ,β)-convexity and (θ,β)-concavity with hypersoft settings [PDF]
Big Data and Computing Visions, 2023 Sub-attribute-valued sets are occasionally viewed as more significant in real-life circumstances than a single set of attributes. The current models that deal with ambiguity and uncertainty, or soft sets, are insufficient to address such situations.
Atiqe Ur Rahman
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Typical Convex Sets of Convex Sets [PDF]
Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1987 There exists a natural notion of convexity in the space of all compact convex sets in D. Thus, we may consider the space of all bounded closed convex families of compact convex sets. We present here a strange generic extremal behaviour of the elements of this space.
T. Schwarz, Tudor Zamfirescu
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Some Properties of Certain Subclass of Meromorphic Functions Associated with $(p , q)$-derivative [PDF]
Sahand Communications in Mathematical Analysis, 2020 In this paper, by making use of $(p , q) $-derivative operator we introduce a new subclass of meromorphically univalent functions. Precisely, we give a necessary and sufficient coefficient condition for functions in this class.
Mohammad Hassan Golmohammadi +2 more
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Non-Linear Inner Structure of Topological Vector Spaces
Mathematics, 2021 Inner structure appeared in the literature of topological vector spaces as a tool to characterize the extremal structure of convex sets. For instance, in recent years, inner structure has been used to provide a solution to The Faceless Problem and to ...
Francisco Javier García-Pacheco +3 more
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Convex Sets and Chebyshev Sets.
MATHEMATICA SCANDINAVICA, 1965 Arne Bronsted
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