scholarly journals Fixed Point Free Actions of Groups of Exponent 5

2004 ◽  
Vol 77 (3) ◽  
pp. 297-304 ◽  
Author(s):  
Enrico Jabara
Keyword(s):  
Fixed Point ◽  
Vector Space ◽  
Regular Subgroup ◽  
Free Actions

AbstractIn this paper we prove that if V is a vector space over a field of positive characteristric p ≠ 5 then any regular subgroup A of exponent 5 of GL(V) is cyclic. As a consequence a conjecture of Gupta and Mazurov is proved to be true.

A NOTE ON FIXED-POINT-FREE ACTIONS OF FINITE GROUPS

1990 ◽  
Vol 41 (2) ◽  
pp. 127-130 ◽  
Author(s):  
S. D. BELL ◽  
B. HARTLEY
Keyword(s):  
Fixed Point ◽  
Finite Groups ◽  
Free Actions

Uniqueness of Free Actions on S3 Respecting a Knot

1987 ◽  
Vol 39 (4) ◽  
pp. 969-982 ◽  
Author(s):  
Michel Boileau ◽  
Erica Flapan
Keyword(s):  
Fixed Point ◽  
Cyclic Group ◽  
Group Action ◽  
Cyclic Groups ◽  
Finite Cyclic Group ◽  
Cyclic Group Action ◽  
Periodic Diffeomorphisms ◽  
Free Actions

In this paper we consider free actions of finite cyclic groups on the pair (S3, K), where K is a knot in S3. That is, we look at periodic diffeo-morphisms f of (S3, K) such that fn is fixed point free, for all n less than the order of f. Note that such actions are always orientation preserving. We will show that if K is a non-trivial prime knot then, up to conjugacy, (S3, K) has at most one free finite cyclic group action of a given order. In addition, if all of the companions of K are prime, then all of the free periodic diffeo-morphisms of (S3, K) are conjugate to elements of one cyclic group which acts freely on (S3, K). More specifically, we prove the following two theorems.THEOREM 1. Let K be a non-trivial prime knot. If f and g are free periodic diffeomorphisms of (S3, K) of the same order, then f is conjugate to a power of g.

scholarly journals The Fixed Point Method for Fuzzy Approximation of a Functional Equation Associated with Inner Product Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
H. Khodaei
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Vector Space ◽  
Fixed Point Method ◽  
Inner Product ◽  
Product Spaces ◽  
Real Vector ◽  
Fixed Integer ◽  
Inner Product Spaces ◽  
Fuzzy Approximation

Th. M. Rassias (1984) proved that the norm defined over a real vector space is induced by an inner product if and only if for a fixed integer holds for all The aim of this paper is to extend the applications of the fixed point alternative method to provide a fuzzy stability for the functional equation which is said to be a functional equation associated with inner product spaces.

scholarly journals On some theorems of Tarafdar

1976 ◽  
Vol 15 (2) ◽  
pp. 213-221
Author(s):  
S.A. Husain ◽  
V.M. Sehgal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Vector Space ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Locally Convex ◽  
Common Fixed Point Theorem

In a recent paper (Bull. Austral. Math. Soc. 13 (1975), 241–245), Tarafdar has considered nonexpansive self mappings on a subset X of a locally convex vector space E and proved an extension to E of a theorem of Göhde. The purpose of this paper is to show that the condition f: X → X, in Göhde-Tarafdar's Theorem in the above paper, may be weakened to f: X → E with f(∂X) ⊆ X. As a consequence, it is further shown that an extension to E of a well-known common fixed point theorem of Belluce and Kirk due to Tarafdar remains true on domains that are not necessarily bounded or quasi-complete.

scholarly journals Two fixed point theorems and invariant integrals

1974 ◽  
Vol 11 (1) ◽  
pp. 15-30 ◽  
Author(s):  
T.J. Cooper ◽  
J.H. Michael
Keyword(s):  
Fixed Point ◽  
Vector Space ◽  
Fixed Point Theorems ◽  
Normed Vector Space ◽  
Invariant Integrals ◽  
Lower Semi ◽  
Normed Vector

Two fixed point theorems for a subset C of a normed vector space X are established by using the concept of centre. These results differ from previous fixed point theorems in that X is assumed to have a topology T as well as a norm. The norm is required to be lower semi-continuous with respect to T and C is required to be convex, bounded with respect to the norm and compact with respect to T.

scholarly journals Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems

2010 ◽  
Vol 2010 (1) ◽  
pp. 170253 ◽  
Author(s):  
Zoran Kadelburg ◽  
Stojan Radenović ◽  
Vladimir Rakočević
Keyword(s):  
Fixed Point ◽  
Vector Space ◽  
Topological Vector Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Cone Metric Spaces ◽  
Cone Metric

Inequivalent, bordant group actions on a surface

1986 ◽  
Vol 99 (2) ◽  
pp. 233-238 ◽  
Author(s):  
Charles Livingston
Keyword(s):  
Fixed Point ◽  
Finite Groups ◽  
Group Actions ◽  
Free Actions ◽  
Orientable Surfaces

An action of a group, G, on a surface, F, consists of a homomorphismø: G → Homeo (F).We will restrict our discussion to finite groups acting on closed, connected, orientable surfaces, with ø(g) orientation-preserving for all g ε G. In addition we will consider only effective (ø is injective) free actions. Free means that ø(g) is fixed-point-free for all g ε G, g ≠ 1. This paper addresses the classification of such actions.

scholarly journals Finite groups without fixed-point-free actions on a disk.

1974 ◽  
Vol 20 (4) ◽  
pp. 349-351
Author(s):  
Richard Parris
Keyword(s):  
Fixed Point ◽  
Finite Groups ◽  
Free Actions

SLICED Ga ACTIONS

2001 ◽  
Vol 11 (01) ◽  
pp. 19-24
Author(s):  
JAMES K. DEVENEY ◽  
DAVID R. FINSTON
Keyword(s):  
Fixed Point ◽  
Characteristic Zero ◽  
Affine Space ◽  
Additive Group ◽  
Invariant Ring ◽  
Three Space ◽  
Free Actions

Let k be a field of characteristic zero. Certain classes of fixed point free actions of the additive group of k on affine n-space over k are known to be conjugate to global translations (i.e. to admit equivariant slices). These classes include actions on complex three space for which the invariant ring contains a variable, and certain generalizations of such actions to affine space of any dimension. Methods to construct an equivariant slice for these classes are presented.

Convergence of iterates and differentiability

1972 ◽  
Vol 14 (3) ◽  
pp. 269-273
Author(s):  
Francis J. Papp ◽  
Robert M. Nielsen
Keyword(s):  
Fixed Point ◽  
Vector Space ◽  
Topological Vector Space ◽  
Sufficient Conditions ◽  
Real Variable ◽  
Limit Function ◽  
Locally Convex

Given a function T mapping a Hausdorff locally convex topological vector space Φ into Φ and a point φ0 of Φ, convergence of the elementary filter associated with the sequence of iterates determined by T and φ0 is investigated. Sufficient conditions that the limit φ if it exists, be a fixed point of T are given and in the case Φ is the space of real valued functions of a real variable differentiability of the limit function φ is investigated.

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