scholarly journals A new class of polynomially convex sets

1991 ◽  
Vol 29 (1-2) ◽  
pp. 51-62 ◽  
Author(s):  
F. Forstnerič ◽  
E. L. Stout
Keyword(s):  
Convex Sets ◽  
New Class ◽  
Polynomially Convex

scholarly journals A Characterization of Polynomially Convex Sets in Banach Spaces

2017 ◽  
Vol 72 (4) ◽  
pp. 2013-2021
Author(s):  
Mortaza Abtahi ◽  
Sara Farhangi
Keyword(s):  
Banach Spaces ◽  
Convex Sets ◽  
Polynomially Convex

scholarly journals Strategyproof and Fair Matching Mechanism for Union of Symmetric M-convex Constraints

2018 ◽  
Author(s):  
Yuzhe Zhang ◽  
Kentaro Yahiro ◽  
Nathanaël Barrot ◽  
Makoto Yokoo
Keyword(s):  
Convex Sets ◽  
Real Life ◽  
Convex Constraints ◽  
New Class ◽  
Distributional Constraints ◽  
Deferred Acceptance ◽  
Matching Mechanism

In this paper, we identify a new class of distributional constraints defined as a union of symmetric M-convex sets, which can represent a variety of real-life constraints in two-sided matching settings. Since M-convexity is not closed under union, a union of symmetric M-convex sets does not belong to this well-behaved class of constraints in general. Thus, developing a fair and strategyproof mechanism that can handle this class is challenging. We present a novel mechanism called Quota Reduction Deferred Acceptance (QRDA), which repeatedly applies the standard DA mechanism by sequentially reducing artificially introduced maximum quotas. We show that QRDA is fair and strategyproof when handling a union of symmetric M-convex sets. Furthermore, in comparison to a baseline mechanism called Artificial Cap Deferred Acceptance (ACDA), QRDA always obtains a weakly better matching for students and, experimentally, performs better in terms of nonwastefulness.

scholarly journals A new class of fractional type set-valued functions

2019 ◽  
Vol 35 (1) ◽  
pp. 79-84
Author(s):  
ALEXANDRU ORZAN ◽  
Keyword(s):  
Special Class ◽  
Convex Sets ◽  
Linear Spaces ◽  
New Class ◽  
Finite Dimensional ◽  
Affine Functions ◽  
Real Linear ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Fractional Type

The so-called ratios of affine functions, introduced by Rothblum (1985) in the framework of finite-dimensional Euclidean spaces, represent a special class of fractional type vector-valued functions, which transform convex sets into convex sets. The aim of this paper is to show that a similar convexity preserving property holds within a new class of fractional type set-valued functions, acting between any real linear spaces.

scholarly journals On some characterizations of sub-b-s-convex functions

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3885-3895 ◽  
Author(s):  
Jiagen Liao ◽  
Tingsong Du
Keyword(s):  
Convex Functions ◽  
Convex Sets ◽  
Sufficient Conditions ◽  
Generalized Convex Functions ◽  
Basic Properties ◽  
New Class ◽  
Constrained Programming

A new class of generalized convex functions called sub-b-s-convex functions is defined by modulating the definitions of s-convex functions and sub-b-convex functions. Similarly, a new class sub-bs-convex sets, which are generalizations of s-convex sets and sub-b-convex sets, is introduced. Furthermore, some basic properties of sub-b-s-convex functions in both general case and differentiable case are presented. In addition the sufficient conditions of optimality for both unconstrained and inequality constrained programming are established and proved under the sub-b-s-convexity.

scholarly journals Analysis of Stokes system with solution-dependent subdifferential boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jing Zhao ◽  
Stanisław Migórski ◽  
Sylwia Dudek
Keyword(s):  
Boundary Conditions ◽  
Convex Sets ◽  
Stokes Problem ◽  
Weak Form ◽  
Nonlinear Boundary Conditions ◽  
Slip Condition ◽  
Hemivariational Inequalities ◽  
Navier Slip ◽  
New Class ◽  
Navier Slip Condition

AbstractWe study the Stokes problem for the incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier–Fujita slip condition, and the threshold slip and leak condition of frictional type. The weak form of the problem leads to a new class of variational–hemivariational inequalities on convex sets for the velocity field. Solution existence and the weak compactness of the solution set to the inequality problem are established based on the Schauder fixed point theorem.

Highly noncontinuable functions on polynomially convex sets

1984 ◽  
pp. 173-178
Author(s):  
Józef Siciak
Keyword(s):  
Convex Sets ◽  
Polynomially Convex

scholarly journals Polynomially convex sets

1962 ◽  
Vol 68 (4) ◽  
pp. 382-388 ◽  
Author(s):  
Gabriel Stolzenberg
Keyword(s):  
Convex Sets ◽  
Polynomially Convex

scholarly journals Fixed-point and coincidence theorems for set-valued maps with nonconvex or noncompact domains in topological vector spaces

2003 ◽  
Vol 2003 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Kazimierz Włodarczyk ◽  
Dorota Klim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Convex Sets ◽  
Fundamental Difference ◽  
Vector Spaces ◽  
Intersection Theorem ◽  
Compact Sets ◽  
Topological Vector Spaces ◽  
New Class ◽  
Coincidence Theorems

A technique, based on the investigations of the images of maps, for obtaining fixed-point and coincidence results in a new class of maps and domains is described. In particular, we show that the problem concerning the existence of fixed points of expansive set-valued maps and inner set-valued maps on not necessarily convex or compact sets in Hausdorff topological vector spaces has a solution. As a consequence, we prove a new intersection theorem concerning not necessarily convex or compact sets and its applications. We also give new coincidence and section theorems for maps defined on not necessarily convex sets in Hausdorff topological vector spaces. Examples and counterexamples show a fundamental difference between our results and the well-known ones.

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