scholarly journals Hecke invariants of knot groups

1974 ◽  
Vol 15 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Robert Riley
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Integral Domain ◽  
Unique Fixed Point ◽  
Projective Line ◽  
Transcendence Degree ◽  
Quotient Field ◽  
Prime Field ◽  
Projective Transformations ◽  
The Right

For each characteristic p, let Fp be the prime field and let Ώp be a fixed universal field which is algebraically closed and of infinite transcendence degree over Fp. When p = 0 we take Ώp = ℂ. Let F be a subfield of Ώp and let R be an integral domain whose quotient field is F. We abbreviate SL(2, R), PGL(2, R), PSL(2, R) to SL(R), PGL(R), PSL(R) respectively, and we cohsider PSL(R) as a group of projective transformations of the projective line ℘(Ώp) and of the “subline” ℘(F) ⊂ ℘(ΏP). The elements of PSL(R) are classified by the number of fixed points they have on ℘(F). If x ∈ PSL(R) has one such fixed point P, then P is the unique fixed point of x on ℘(ΏP) and x is called parabolic. All other x (except the identity E) have two distinct fixed points on ℘(Ώp) and x is called hyperbolic if these are on ℘(F), and elliptic otherwise. We put symbols for operators on the right.

scholarly journals Groups generated by elements with rational fixed points

1997 ◽  
Vol 40 (1) ◽  
pp. 19-30 ◽  
Author(s):  
A. W. Mason
Keyword(s):  
Normal Subgroup ◽  
Fixed Points ◽  
Large Class ◽  
Integral Domain ◽  
Structure Theorem ◽  
Quotient Field ◽  
Linear Fractional Transformations ◽  
Krull Domain ◽  
Dedekind Domains ◽  
Precise Version

Let R be a commutative integral domain and let S be its quotient field. The group GL2(R) acts on Ŝ = S ∪ {∞} as a group of linear fractional transformations in the usual way. Let F2(R, z) be the stabilizer of z ∈ Ŝ in GL2(R) and let F2(R) be the subgroup generated by all F2(R, z). Among the subgroups contained in F2(R) are U2(R), the subgroup generated by all unipotent matrices, and NE2(R), the normal subgroup generated by all elementary matrices.We prove a structure theorem for F2(R, z), when R is a Krull domain. A more precise version holds when R is a Dedekind domain. For a large class of arithmetic Dedekind domains it is known that the groups NE2(R),U2(R) and SL2(R) coincide. An example is given for which all these subgroups are distinct.

scholarly journals Fixed point theorems in modular G-metric spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Daniel Francis ◽  
Manuel de la Sen ◽  
Mujahid Abbas
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Weakly Compatible ◽  
Special Cases

AbstractWe prove the existence and uniqueness of fixed points of some generalized contractible operators defined on modular G-metric spaces and also prove the modular G-continuity of such operators. Furthermore, we prove that some generalized weakly compatible contractive operators in modular G-metric spaces have a unique fixed point. Our results extend, generalize, complement and include several known results as special cases.

scholarly journals Unique Fixed Point Theorem for Weakly C-Contractive Mappings

1970 ◽  
Vol 5 (1) ◽  
pp. 6-13 ◽  
Author(s):  
Binayak S Choudhury
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Metric Space ◽  
Metric Spaces ◽  
Unique Fixed Point ◽  
Complete Metric Spaces ◽  
Contractive Mappings ◽  
Engineering And Technology ◽  
Existing Result

In this work we introduce the class of weakly c-contractive mappings. We establish that these mappings necessarily have unique fixed points in complete metric spaces. We support our result by an example. Our result also generalises an existing result in metric spaces. Key words: Metric space; Fixed point; Weak C-contraction. M S C (2000): 54H25   DOI: 10.3126/kuset.v5i1.2842 Kathmandu University Journal of Science, Engineering and Technology Vol.5, No.1, January 2009, pp 6-13

scholarly journals Fixed Points for Multivalued Convex Contractions on Nadler Sense Types in a Geodesic Metric Space

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 155 ◽  
Author(s):  
Amelia Bucur
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Complete Metric Space ◽  
Hausdorff Metric ◽  
Geodesic Metric Space ◽  
Geodesic Metric ◽  
Convex Contractions ◽  
The Right ◽  
Multivalued Contractions

In 1969, based on the concept of the Hausdorff metric, Nadler Jr. introduced the notion of multivalued contractions. He demonstrated that, in a complete metric space, a multivalued contraction possesses a fixed point. Later on, Nadler’s fixed point theorem was generalized by many authors in different ways. Using a method given by Angrisani, Clavelli in 1996 and Mureşan in 2002, we prove in this paper that, for a class of convex multivalued left A-contractions in the sense of Nadler and the right A-contractions with a convex metric, the fixed points set is non-empty and compact. In this paper we present the fixed point theorems for convex multivalued left A-contractions in the sense of Nadler and right A-contractions on the geodesic metric space. Our results are particular cases of some general theorems, to the multivalued left A-contractions in the sense of Nadler and right A-contractions, and particular cases of the results given by Rus (1979, 2008), Nadler (1969), Mureşan (2002, 2004), Bucur, Guran and Petruşel (2009), Petre and Bota (2013), etc., and are applicable in many fields, such as economy, management, society, biology, ecology, etc.

scholarly journals Recent Advances on the Results for Nonunique Fixed in Various Spaces

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 72
Author(s):  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Unique Fixed Point ◽  
Recent Advances ◽  
Short Survey ◽  
Abstract Spaces

In this short survey, we aim to underline the importance of the non-unique fixed point results in various abstract spaces. We recall a brief background on the topic and we combine, collect and unify several existing non-unique fixed points in the literature. Some interesting examples are considered.

Some non-unique fixed point theorems of Ćirić type using rational-type contractive conditions

2017 ◽  
Vol 24 (3) ◽  
pp. 455-461 ◽  
Author(s):  
Memudu Olaposi Olatinwo
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Unique Fixed Point ◽  
Comparison Functions ◽  
Rational Type

AbstractIn this paper, we prove some fixed point theorems of Ćirić type for mappings having non-unique fixed points by employing rational-type contractive conditions and the notion of comparison functions. Our results are generalizations, extensions and improvements of some previous and corresponding results in the literature.

scholarly journals Approximating fixed points of nonexpansive type mappings

2001 ◽  
Vol 26 (3) ◽  
pp. 183-188
Author(s):  
Hemant K. Pathak ◽  
Mohammad S. Khan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Unique Fixed Point ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex

In a uniformly convex Banach space, the convergence of Ishikawa iterates to a unique fixed point is proved for nonexpansive type mappings under certain conditions.

scholarly journals THE ASYMPTOTIC BEHAVIOR OF TRAJECTORIES OF DISSIPATIVE QUADRATIC STOCHASTIC OPERATORS ON 2D SIMPLEX

2012 ◽  
Vol 09 ◽  
pp. 293-298
Author(s):  
FARRUH SHAHIDI ◽  
ABU OSMAN MD TAP
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Fixed Points ◽  
Unique Fixed Point ◽  
Limit Behavior ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Quadratic Stochastic Operators ◽  
The Face

In the present paper we study limit behavior of dissipative quadratic stochastic operators on 2D simplex. We show that dissipative quadratic stochastic operator, which is not linear, is either regular or has infinitely many fixed points. If dissipative quadratic stochastic operator is regular, it is shown that its unique fixed point is either a vertex of the simplex or the center of the face of the simplex.

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.

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