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**Date:** 2017
**Subject:** 0101 Pure Mathematics | 0102 Applied Mathematics | Topological group | Locally compact group | pro-Lie group | Separable topological space
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/159323
**Description:** We give a complete characterization of subgroups of separable topological groups. Then we show that the following conditions are equivalent for an omega-narrow topological group G: (i) G is homeomorph... More
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**Date:** 2017
**Subject:** 0101 Pure Mathematics | Barreled space | Free locally convex space | Free topological vector space | kω-Space
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/156253
**Description:** In this paper the free topological vector space V(X) over a Tychonoff space X is defined and studied. It is proved that V(X) is a kω-space if and only if X is a kω-space. If X is infinite, then V(X) c... More
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**Date:** 2017
**Subject:** 0101 Pure Mathematics | Locally convex topological vector space | Separable topological space
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154574
**Description:** In 1983 P. Domanski investigated the question: For which separable topological vector spaces E, does the separable space have a nonseparable closed vector subspace, where is the cardinality of the con... More
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**Date:** 2017
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/156932
**Description:** A class of abelian topological groups was previously defined to be a variety of topological groups with coproducts if it is closed under forming subgroups, quotients, products and coproducts in the ca... More
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**Date:** 2017
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/155253
**Description:** In this paper the relation between the weak subdifferentials and the directional derivatives, as well as optimality conditions for nonconvex optimization problems in reflexive Banach spaces, are inves... More
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**Date:** 2016
**Subject:** 0101 Pure Mathematics | Pro-Lie group | Locally compact abelian group | Open mapping theorem
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154692
**Description:** It is proved that any surjective morphism f : Z(k) -> K onto a locally compact group K is open for every cardinal k. This answers a question posed by Hofmann and the second author.
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**Date:** 2016
**Subject:** 0101 Pure Mathematics | 0102 Applied Mathematics | 0906 Electrical and Electronic Engineering | Borwein-Preiss variational principle | Smooth variational principle | Gauge-type function | Perturbation
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100317
**Description:** In this article, we refine and slightly strengthen the metric space version of the Borwein-Preiss variational principle due to Li and Shi (2000) [12], clarify the assumptions and conclusions of their ... More
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**Date:** 2016
**Subject:** 0101 Pure Mathematics | 0802 Computation Theory and Mathematics | Compact groups | Subgroups
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/99916
**Description:** In 1985 S. Saeki and K. Stromberg published the following question: Does every infinite compact group have a subgroup which is not Haar measurable? An affirmative answer is given for all compact group... More
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**Date:** 2016
**Subject:** 0101 Pure Mathematics | Cournot-Nash-Walras equilibrium | Existence | MOPEC | Stability | Stationarity conditions
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/102916
**Description:** This paper concerns a model of Cournot-Nash-Walras (CNW) equilibrium where the Cournot-Nash concept is used to capture equilibrium of an oligopolistic market with non-cooperative players/firms who sha... More
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**Date:** 2016
**Subject:** 0101 Pure Mathematics | Alternating projections | Uniform regularity | Normal cone | Subdifferential
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/154479
**Description:** We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of t... More
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**Date:** 2016
**Subject:** 0101 Pure Mathematics | Convex functions | Fenchel subdifferential | Subdifferential calculus rules | Convex infinite-dimensional | Optimization
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/102487
**Description:** In this paper we establish new rules for the calculus of the subdifferential mapping of the sum of two convex functions. Our results are established under conditions which are at an intermediate level... More
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**Authors:**
Sultanova, Nargiz
**Date:** 2015
**Subject:** 0101 Pure Mathematics | Large-scale problems | Mathematical programming | Nonsmooth optimisation
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/89653
**Description:** Nonsmooth optimisation problems are problems which deal with minimisation or maximisation of functions that are not necessarily differentiable. They arise frequently in many practical applications, fo... More
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**Date:** 2015
**Subject:** 0101 Pure Mathematics | Maximally monotone operator | ε-subdifferential mapping | Subdifferential operator | Convex lower semicontinuous function | Fitzpatrick function | Enlargement of an operator | Brøndsted- Rockafellar enlargements | Additive enlargements | Fenchel-Young function
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/100313
**Description:** We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the ... More
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**Date:** 2015
**Subject:** 0101 Pure Mathematics | Epi-convergence | Epi/hypo convergence | Equivalence class | Lopsided convergence | Partial Legendre-Fenchel transform | Partial skew conjugate
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/89643
**Description:** Epi/hypo convergence of finite-valued bivariate functions defined on the product of two subsets, with some connections to lopsided convergence, is considered. Namely, we deal with three full character... More
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**Authors:**
Kruger, Alexander
**Date:** 2015
**Subject:** 0101 Pure Mathematics | Error bounds | Hölder metric subregularity | Metric regularity | Metric subregularity | Slope
**Type:** Text
**Identifier:** http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/155338
**Description:** The Holder setting of the metric subregularity property of set-valued mappings between general metric or Banach/Asplund spaces is investigated in the framework of the theory of error bounds for extend... More
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