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三亚国际数学论坛：Recent Advances in Convex Geometry and Geometric Functional Analysis
三亚国际数学论坛 Convex Geometry Geometric Functional Analysis
2017/11/24
Convexity is omnipresent in mathematics and the mathematical sciences. During the past ten years, there has been intensive research in convex geometry. Methods and techniques from different fields hav...
Convex optimization of graph Laplacian eigenvalues
Graph theory Laplacian matrix Convex optimization Semidefinite pro-gramming Markov chain Distributed averaging Effective resistance
2015/8/10
We consider the problem of choosing the edge weights of an undirected graph so as to maximize or minimize some function of the eigenvalues of the associated Laplacian matrix, subject to some constrain...
Approximations of convex bodies by polytopes and by projections of spectrahedra
convex body spectrahedron approximation computational complex-ity semidefinite programming
2012/4/18
We prove that for any compact set B in R^d and for any epsilon >0 there is a finite subset X of B of |X|=d^{O(1/epsilon^2)} points such that the maximum absolute value of any linear function ell: R^d ...
On approximation by ∆- convex polyhedron support functions
Weierstrass theorem function approximation weakly continuous function weakly compact set normed semigroup ∆ convex polyhedron support function
2011/10/20
The classical Weierstrass theorem states that every continuous function f defined ona compact set K▲Rn can be uniformly approximated by polynomials. In this paper we show firstthat it is again valid i...
On super weakly compact convex sets and representation of {m swcc}(X)^*
super weakly compact set dual of normed semigroup uniform Fr'echet differetiability representation
2011/10/20
In this note, we give first that a characterization of super weakly compact convex sets of a Banach space X, namely, a sufficient and necessary condition for a closed bounded convex set Ksubset X to b...
New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals
Ostrowski type inequality convex function Riemann-Liouville fractional integral
2011/9/22
Abstract: New identity similar to an identity of [13] for fractional integrals have been defined. Then making use of this identity, some new Ostrowski type inequalities for Riemann-Liouville fractiona...
Characterization of uniformly convex and smooth Banach spaces by using Carleson measures in Bessel settings
BMO Bessel operators Carleson measures uniformly convex uniformly smooth Banach spaces
2011/9/22
Abstract: In this paper we obtain new characterizations of the q-uniformly convex and smooth Banach spaces by using Carleson measures. These measures are defined by Poisson integral associated with Be...
On the Coordinated Convex Functions
Hadamard’s inequality co-ordinates convexity Holder’s inequality Power mean inequality
2011/9/15
Abstract: In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.
On Some New Hadamard-Type Inequalities for Coordinated Quasi-convex Functions
Quasi-convex functions Holder Inequality Power Mean Inequality co-ordinates Lipschitzian function
2011/9/15
Abstract: In this paper, we establish some Hadamard-type inequalities based on coordinated quasi-convexity. Also we define a new mapping associated to coordinated convexity and we prove some propertie...
A complete locally convex space of countable dimension admitting an operator with no invariant subspaces
Cyclic operators invariant subspaces topological vector spaces
2010/12/6
We construct a complete locally convex topological vector space X of countable algebraic dimension and a continuous linear operator T : X → X such that T has no non-trivial closed invariant subspaces.
A Unified Fixed Point Theory in Generalized Convex Spaces
multimap classes $\frak B$ and $\frak A_c^\kappa$ $\Phi$-map $\Phi$-set $\Phi$-space admissible $G$-convex space the Zima type locally $G$-convex space $LG$-space
2007/12/10
Let $\frak B$ be the class of `better' admissible multimaps due to the author. We introduce new concepts of admissibility (in the sense of Klee) and of Klee approximability for subsets of $G$-convex u...