scholarly journals Word equations in non-deterministic linear space

2021 ◽  
Author(s):  
Artur Jeż
Keyword(s):  
Linear Space ◽  
Word Equations

Processing uncertain information in the linear space of fuzzy sets

1991 ◽  
Vol 44 (2) ◽  
pp. 187-198 ◽  
Author(s):  
Wladyslaw Homenda ◽  
Witold Pedrycz
Keyword(s):  
Fuzzy Sets ◽  
Linear Space ◽  
Uncertain Information

scholarly journals Injection of a self-consistent beam with linear space charge force into a ring

2018 ◽  
Vol 21 (12) ◽  
Author(s):  
J. A. Holmes ◽  
T. Gorlov ◽  
N. J. Evans ◽  
M. Plum ◽  
S. Cousineau
Keyword(s):  
Space Charge ◽  
Linear Space ◽  
Self Consistent

scholarly journals Spectral Transformations and Associated Linear Functionals of the First Kind

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 107
Author(s):  
Juan Carlos García-Ardila ◽  
Francisco Marcellán
Keyword(s):  
Orthogonal Polynomials ◽  
Linear Space ◽  
Linear Functional ◽  
Linear Functionals ◽  
Spectral Transformations ◽  
Christoffel Transformation ◽  
Complex Coefficients

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients, let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For a canonical Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0, and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for canonical Geronimus transformations.

scholarly journals Fixed points of quasi-nonexpansive mappings

1972 ◽  
Vol 13 (2) ◽  
pp. 167-170 ◽  
Author(s):  
W. G. Dotson
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Linear Space ◽  
Complex Plane ◽  
Normed Linear Space ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
The Other ◽  
Commuting Mappings ◽  
Analytic Mappings

A self-mapping T of a subset C of a normed linear space is said to be non-expansive provided ║Tx — Ty║ ≦ ║x – y║ holds for all x, y ∈ C. There has been a number of recent results on common fixed points of commutative families of nonexpansive mappings in Banach spaces, for example see DeMarr [6], Browder [3], and Belluce and Kirk [1], [2]. There have also been several recent results concerning common fixed points of two commuting mappings, one of which satisfies some condition like nonexpansiveness while the other is only continuous, for example see DeMarr [5], Jungck [8], Singh [11], [12], and Cano [4]. These results, with the exception of Cano's, have been confined to mappings from the reals to the reals. Some recent results on common fixed points of commuting analytic mappings in the complex plane have also been obtained, for example see Singh [13] and Shields [10].

On the convex kernel of a compact set

1967 ◽  
Vol 63 (2) ◽  
pp. 311-313 ◽  
Author(s):  
D. G. Larman
Keyword(s):  
Linear Space ◽  
Compact Subset ◽  
Line Segment ◽  
Linear Dimension ◽  
Single Point ◽  
Compact Set ◽  
Topological Linear Space ◽  
Topological Linear

Suppose that E is a compact subset of a topological linear space ℒ. Then the convex kernel K, of E, is such that a point k belongs to K if every point of E can be seen, via E, from k. Valentine (l) has asked for conditions on E which ensure that the convex kernel K, of E, consists of exactly one point, and in this note we give such a condition. If A, B, C are three subsets of E, we use (A, B, C) to denote the set of those points of E, which can be seen, via E, from a triad of points a, b, c, with a ∈ A, b ∈ B, c ∈ C. We shall say that E has the property if, whenever A is a line segment and B, C are points of E which are not collinear with any point of A, the set (A, B, C) has linear dimension of at most one, and degenerates to a single point whenever A is a point.

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