Hyperspaces of Topological Vector Spaces: Their Embedding in Topological Vector Spaces

Prakash, Prem; Sertel, Murat R.

doi:10.2307/2041686

Cited by 12 publications

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“…After, Prakash-Sertel [40,41] generalized the above result. In [2], the author rewrote the following forms using set order relations.…”

Section: Proposition 32 ([42]mentioning

confidence: 82%

A new minimal element theorem and generalized Ekeland’s variational principle in complete lattice optimization problem

Araya,

2024

Preprint

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In this paper, we first introduce some types of set relations on the power set of n-dimensional Euclidean spaces which are proposed by Kuroiwa-Tanaka-Ha and Jahn-Ha. We also mension new types of cancellation laws of set relations. Second, we introduce a complete lattice-valued problem on the power set of n-dimensional Euclidean spaces proposed by Hamel et al. Applying nonlinear scalrizing technique in complete lattice, we present a new type of minimal element theorem and generalized Ekeland’s variational principle in complete lattice optimization problem. AMS Subject Classification: 06B23, 06F30, 49J53, 58E17.

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“…After, Prakash-Sertel [40,41] generalized the above result. In [2], the author rewrote the following forms using set order relations.…”

Section: Proposition 32 ([42]mentioning

confidence: 82%

A new minimal element theorem and generalized Ekeland’s variational principle in complete lattice optimization problem

Araya,

2024

Preprint

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“…Roughly speaking, they are 1-dimensional "semi-vector" spaces. This concept is not new, and has been used in contexts which differ a lot from the present one: for instance, see [4] for the analysis of some properties of Z 2 -valued matrices, [12] for problems of fuzzy analysis, [28] for problems of measure theory, [29,30] for topological fixed point problems. Then, we introduce the sesqui-tensor product of a semi-vector space with a vector space and the semi-tensor product between semi-vector spaces.…”

Section: Summary Of the Present Papermentioning

confidence: 99%

An Algebraic Approach to Physical Scales

Janyška

Modugno

Vitolo³

2009

Acta Appl Math

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This paper is aimed at introducing an algebraic model for physical scales and units of measurement. This goal is achieved by means of the concept of "positive space" and its rational powers. Positive spaces are "semi-vector spaces" on which the group of positive real numbers acts freely and transitively through the scalar multiplication. Their tensor multiplication with vector spaces yields "scaled spaces" that are suitable to describe spaces with physical dimensions mathematically. We also deal with scales regarded as fields over a given background (e.g., spacetime).

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“…Finally, another close relative of a conlinear space is a semivector space in the sense of [169]. P. Prakash and M. R. Sertel (see also [170]) defined this structure in the early Seventies and observed that the collections of non-empty and non-empty convex sets of a vector space form a semivector spaces. In a semivector space, the existence of a neutral element with respect to the addition is not required.…”

Section: Comments On Conlinear Spaces and Residuationmentioning

confidence: 99%

Set Optimization—A Rather Short Introduction

Hamel

Heyde

Löhne

et al. 2015

Springer Proceedings in Mathematics &Amp; Statistics

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Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for setand vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems.

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Hyperspaces of Topological Vector Spaces: Their Embedding in Topological Vector Spaces

Cited by 12 publications

References 0 publications

A new minimal element theorem and generalized Ekeland’s variational principle in complete lattice optimization problem

A new minimal element theorem and generalized Ekeland’s variational principle in complete lattice optimization problem

An Algebraic Approach to Physical Scales

Set Optimization—A Rather Short Introduction

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