Fixed points on rotating continua

1954 ◽  
Vol 50 (1) ◽  
pp. 1-7
Author(s):  
E. R. Reifenberg
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Single Domain ◽  
Image Position ◽  
Prime End ◽  
Plane Continuum ◽  
The Continuum

Suppose I is a bounded plane continuum whose complement is a single domain (I) and that is a (1–1) bicontinuous transformation of the plane onto itself which leaves I invariant. Cartwright and Littlewood(1) have proved the following theorem:Theorem A. Suppose that(I) has no prime end fixed underand the frontier of I contains a fixed point P. Ifis any prime end of(I) containing P, and C is any curve in(I) converging tosuch that PeC¯, the closure of C, then for some‡ integer N the continuum I(FN) consisting oftogether with the sum B(FN) of its interior complementary domains contains all fixed points in I.

scholarly journals KRASNOSELSKI–MANN ITERATION FOR HIERARCHICAL FIXED POINTS AND EQUILIBRIUM PROBLEM

2009 ◽  
Vol 79 (2) ◽  
pp. 187-200 ◽  
Author(s):  
GIUSEPPE MARINO ◽  
VITTORIO COLAO ◽  
LUIGI MUGLIA ◽  
YONGHONG YAO
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Mann Iteration ◽  
Type Method ◽  
Equilibrium Function ◽  
Hierarchical Fixed Point ◽  
Image Position ◽  
Mann Type Method ◽  
Hierarchical Fixed Point Problems

AbstractWe give an explicit Krasnoselski–Mann type method for finding common solutions of the following system of equilibrium and hierarchical fixed points: where C is a closed convex subset of a Hilbert space H, G:C×C→ℝ is an equilibrium function, T:C→C is a nonexpansive mapping with Fix(T) its set of fixed points and f:C→C is a ρ-contraction. Our algorithm is constructed and proved using the idea of the paper of [Y. Yao and Y.-C. Liou, ‘Weak and strong convergence of Krasnosel’skiĭ–Mann iteration for hierarchical fixed point problems’, Inverse Problems24 (2008), 501–508], in which only the variational inequality problem of finding hierarchically a fixed point of a nonexpansive mapping T with respect to a ρ-contraction f was considered. The paper follows the lines of research of corresponding results of Moudafi and Théra.

A differential equation for undamped forced non-linear oscillations. II

1958 ◽  
Vol 54 (4) ◽  
pp. 426-438 ◽  
Author(s):  
G. R. Morris
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Stationary Points ◽  
Original Form ◽  
Topological Transformation ◽  
Non Linear ◽  
Image Position ◽  
Special Case

In a previous paper of the same title (1) onwhere e(t) is even and has least period 2π, I have shown that the equation has a family of periodic solutions or, equivalently, that a topological transformation T has a family of fixed points. Since much of the detail in (1) is irrelevant here, it will be convenient if the results we must quote about are put into the following form:Theoerm A. There is a constant integer p such that, whenever k ≥ p, there is at least one solution xk(t) of (1·1) for which(i) xk(0) > 0, ẋk(0) = 0 and xk(t) has period 2π;(ii) xk(t) = xk(2π–t);(iii) xk(t) has, in 0 ≤ t < 2π, k positive maxima, k negative minima and no other stationary points;(iv) This except (ii), is a special case of Theorem 2 with the notation x*(t|k, 1, 0) simplified to xk(t) and the constant p introduced to guarantee that (vi) of Theorem 2 implies (iv) above. Finally Lemma 1 of (1), in its original form or as specialized in Theorem B (i) below, gives (ii).We shall write ak = xk(0) and note, though we do not need to use it here, that, by (v) of Theorem 2, ak = kw + O(k−2) as k→ ∞. If Fk denotes the point (ak, 0) of the (a, b)-plane then Fk is a fixed point of T and we can best state this paper's results in terms of the segment joining a pair of such points.

scholarly journals Fixed Points can Characterise Curves

1978 ◽  
Vol 21 (2) ◽  
pp. 207-211 ◽  
Author(s):  
Helga Schirmer
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Simple Closed Curve ◽  
Closed Curve ◽  
The Given ◽  
The Continuum

AbstractThe concept of a firm fixed point of a selfmap of a metric space is introduced. Loosely speaking a fixed point is firm if it cannot be moved to a point nearby with the help of a map which is arbitrarily close to the given map. It is shown that a continuum always admits a selfmap with a firm fixed point if the continuum contains a triod and if the vertex of the triod has a neighbourhood which is a dendrite. This condition holds in particular for local dendrites. Hence a local dendrite is an arc or a simple closed curve if and only if it does not admit a selfmap which has a firm fixed point.

On H-balls and canonical regions of loxodromic elements in complex hyperbolic space

1993 ◽  
Vol 113 (3) ◽  
pp. 573-582 ◽  
Author(s):  
Shigeyasu Kamiya
Keyword(s):  
Fixed Point ◽  
Automorphism Group ◽  
Unit Ball ◽  
Fixed Points ◽  
Hyperbolic Space ◽  
Hermitian Form ◽  
Complex Hyperbolic Space ◽  
Trivial Element ◽  
Image Position

Let U(1, n; ℂ) be the automorphism group of the Hermitian formfor . We can regard an element of U(1, n; ℂ) as a transformation acting on , where is the closure of the complex unit ballThe non-trivial elements of U(1, n; ℂ) fall into three conjugacy types, depending on the number and the location of their fixed points. Let g be a non-trivial element of U(1, n; ℂ). We call g elliptic if it has a fixed point in Bn and g parabolic if it has exactly one fixed point and this lies on the boundary ∂Bn. An element g will be called loxodromic if it has exactly two fixed points and they lie on ∂Bn.

LARGE CARDINALS AND LIGHTFACE DEFINABLE WELL-ORDERS, WITHOUT THE GCH

2015 ◽  
Vol 80 (1) ◽  
pp. 251-284
Author(s):  
SY-DAVID FRIEDMAN ◽  
PETER HOLY ◽  
PHILIPP LÜCKE
Keyword(s):  
Fixed Point ◽  
Measurable Cardinal ◽  
Large Cardinals ◽  
Inaccessible Cardinal ◽  
Proper Class ◽  
Supercompact Cardinals ◽  
Image Position ◽  
Class Forcing ◽  
Continuum Function ◽  
The Continuum

AbstractThis paper deals with the question whether the assumption that for every inaccessible cardinal κ there is a well-order of H(κ+) definable over the structure $\langle {\rm{H}}({\kappa ^ + }), \in \rangle$ by a formula without parameters is consistent with the existence of (large) large cardinals and failures of the GCH. We work under the assumption that the SCH holds at every singular fixed point of the ℶ-function and construct a class forcing that adds such a well-order at every inaccessible cardinal and preserves ZFC, all cofinalities, the continuum function, and all supercompact cardinals. Even in the absence of a proper class of inaccessible cardinals, this forcing produces a model of “V = HOD” and can therefore be used to force this axiom while preserving large cardinals and failures of the GCH. As another application, we show that we can start with a model containing an ω-superstrong cardinal κ and use this forcing to build a model in which κ is still ω-superstrong, the GCH fails at κ and there is a well-order of H(κ+) that is definable over H(κ+) without parameters. Finally, we can apply the forcing to answer a question about the definable failure of the GCH at a measurable cardinal.

Some Fixed and Common Fixed Point Theorems in Metric Spaces

1974 ◽  
Vol 17 (2) ◽  
pp. 257-259 ◽  
Author(s):  
V. M. Sehgal
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Common Fixed Points ◽  
Image Position ◽  
Common Fixed Point Theorems

Let (X, d) be a metric space and Ti(i=l, 2) be self mappings of X. The purpose of this paper is to investigate the fixed and common fixed points of Ti, when the pair Ti(i=l, 2) satisfies a condition of the following type:(1)

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

Coincidence and fixed points for hybrid tangential maps

2010 ◽  
Vol 17 (2) ◽  
pp. 273-285
Author(s):  
Tayyab Kamran ◽  
Quanita Kiran
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Property ◽  
Fixed Point Theorems ◽  
Acta Math ◽  
Contractive Condition ◽  
The Common

Abstract In [Int. J. Math. Math. Sci. 2005: 3045–3055] by Liu et al. the common property (E.A) for two pairs of hybrid maps is defined. Recently, O'Regan and Shahzad [Acta Math. Sin. (Engl. Ser.) 23: 1601–1610, 2007] have introduced a very general contractive condition and obtained some fixed point results for hybrid maps. We introduce a new property for pairs of hybrid maps that contains the property (E.A) and obtain some coincidence and fixed point theorems that extend/generalize some results from the above-mentioned papers.

scholarly journals Solution of Some Impulsive Differential Equations via Coupled Fixed Point

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Author(s):  
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Coupled Fixed Point ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
System Of Differential Equations ◽  
Coupled Fixed Points

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

scholarly journals CONFORMAL HOUSE

2010 ◽  
Vol 25 (24) ◽  
pp. 4603-4621 ◽  
Author(s):  
THOMAS A. RYTTOV ◽  
FRANCESCO SANNINO
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Gauge Group ◽  
Gauge Theories ◽  
Simultaneous Presence ◽  
Consistency Check ◽  
Effective Lagrangian ◽  
Anomalous Dimensions ◽  
Mass Terms

We investigate the gauge dynamics of nonsupersymmetric SU (N) gauge theories featuring the simultaneous presence of fermionic matter transforming according to two distinct representations of the underlying gauge group. We bound the regions of flavors and colors which can yield a physical infrared fixed point. As a consistency check we recover the previously investigated bounds of the conformal windows when restricting to a single matter representation. The earlier conformal windows can be imagined to be part now of the new conformal house. We predict the nonperturbative anomalous dimensions at the infrared fixed points. We further investigate the effects of adding mass terms to the condensates on the conformal house chiral dynamics and construct the simplest instanton induced effective Lagrangian terms.

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