scholarly journals On the James number of cyclic maps of spheres

1984 ◽  
Vol 10 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Kouyemon IRIYE
Keyword(s):  
Cyclic Maps

The Milnor–Stasheff Filtration on Spaces and Generalized Cyclic Maps

2012 ◽  
Vol 55 (3) ◽  
pp. 523-536 ◽  
Author(s):  
Norio Iwase ◽  
Mamoru Mimura ◽  
Nobuyuki Oda ◽  
Yeon Soo Yoon
Keyword(s):  
Projective Spaces ◽  
Intermediate Stage ◽  
Lens Spaces ◽  
Cyclic Maps

AbstractThe concept of Ck-spaces is introduced, situated at an intermediate stage between H-spaces and T-spaces. The Ck-space corresponds to the k-th Milnor–Stasheff filtration on spaces. It is proved that a space X is a Ck-space if and only if the Gottlieb set G(Z, X) = [Z, X] for any space Z with cat Z ≤ k, which generalizes the fact that X is a T-space if and only if G(ΣB, X) = [ΣB, X] for any space B. Some results on the Ck-space are generalized to the -space for a map ƒ : A → X. Projective spaces, lens spaces and spaces with a few cells are studied as examples of Ck-spaces, and non-Ck-spaces.

scholarly journals On Weak Contractive Cyclic Maps in Generalized Metric Spaces and Some Related Results on Best Proximity Points and Fixed Points

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Nonempty Intersection ◽  
Generalized Metric Spaces ◽  
Best Proximity Points ◽  
Generalized Metric ◽  
Cyclic Maps ◽  
Convergence Of Sequences ◽  
Composite Maps ◽  
Decreasing Functions

This paper discusses the properties of convergence of sequences to limit cycles defined by best proximity points of adjacent subsets for two kinds of weak contractive cyclic maps defined by composite maps built with decreasing functions with either the so-calledr-weaker Meir-Keeler orr,r0-stronger Meir-Keeler functions in generalized metric spaces. Particular results about existence and uniqueness of fixed points are obtained for the case when the sets of the cyclic disposal have a nonempty intersection. Illustrative examples are discussed.

scholarly journals On the Best Proximity Points for p–Cyclic Summing Contractions

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1060
Author(s):  
Miroslav Hristov ◽  
Atanas Ilchev ◽  
Boyan Zlatanov
Keyword(s):  
Fixed Point Theory ◽  
Complete Metric Space ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Point Theory ◽  
Picard Iteration ◽  
Best Proximity Points ◽  
Underlying Space ◽  
Cyclic Maps

We present a condition that guarantees the existence and uniqueness of fixed (or best proximity) points in complete metric space (or uniformly convex Banach spaces) for a wide class of cyclic maps, called p–cyclic summing maps. These results generalize some known results from fixed point theory. We find a priori and a posteriori error estimates of the fixed (or best proximity) point for the Picard iteration associated with the investigated class of maps, provided that the modulus of convexity of the underlying space is of power type. We illustrate the results with some applications and examples.

The Homotopy Set of the Axes of Pairings

1990 ◽  
Vol 42 (5) ◽  
pp. 856-868 ◽  
Author(s):  
Nobuyuki Oda
Keyword(s):  
Group Structure ◽  
Homotopy Classes ◽  
Fundamental Properties ◽  
Cyclic Map ◽  
Cyclic Maps ◽  
Image Position

Varadarajan [13] named a map f: A → X a cyclic map when there exists a map F: X × A → X such that for the folding map ∇X: X ∨ X → X. He defined the generalized Gottlieb set G(A, X) of the homotopy classes of the cyclic maps F: A → X and studied the fundamental properties of G(A, X) If A is a co-Hopf space, then the Varadarajan set G(A, X) has a group structure [13]. The group G(A,X) is a generalization of G(X) and Gn(X) of Gottlieb [2,3]. Some authors studied the properties of the Varadarajan set, its dual and related topics [4, 5, 6, 7,12,15,16,17].

On Evaluation Subgroups of Generalized Homotopy Groups

1984 ◽  
Vol 27 (1) ◽  
pp. 78-86 ◽  
Author(s):  
K. L. Lim
Keyword(s):  
Full Subcategory ◽  
Abelian Groups ◽  
Homotopy Groups ◽  
Contravariant Functor ◽  
Homotopy Classes ◽  
Cyclic Maps

AbstractG(A, X) consists of all homotopy classes of cyclic maps from a space A to another space X. If A is an H-cogroup, then G(A, X) is a group. G(A, X) preserves products in the second variable and is a contravariant functor of A from the full subcategory of H-cogroups and maps into the category of abelian groups and homomorphisms. If X is an H-cogroup, then G(X, X) is a ring.

scholarly journals On cyclic maps

1982 ◽  
Vol 32 (3) ◽  
pp. 349-357 ◽  
Author(s):  
K. L. Lim
Keyword(s):  
Finite Order ◽  
Cyclic Maps ◽  
Definition Of ◽  
The Relationship

AbstractThe definition of cyclic maps is recalled and their existence discussed. Among other things, it is shown that cyclicity of maps is closed under product and that if f is cyclic then Ωf is central.Some results of Gottlieb (1972) on homology are applied to investigate the relationship between cyclicity of maps and maps of finite order.

scholarly journals Homotopy actions, cyclic maps and their duals

2005 ◽  
Vol 7 (1) ◽  
pp. 169-184
Author(s):  
Martin Arkowitz ◽  
Gregory Lupton
Keyword(s):  
Cyclic Maps

On cyclic maps

1972 ◽  
Vol 71 (3) ◽  
pp. 449-456 ◽  
Author(s):  
V. P. Snaith
Keyword(s):  
Symmetric Group ◽  
Cartesian Product ◽  
Base Point ◽  
Cyclic Map ◽  
Cyclic Maps

Throughout X will denote a connected, finite C.W. complex.Let G be a subgroup of ∑n, the symmetric group, which acts transitively on the Cartesian product, Xn, of the space X. A map f:Xn→X is G-symmetric if it commutes with the action of G. If x0εX is a base point let i:X→Xn denote the inclusion, i(x) = (x,x0, …,x0). In ((6); (7); (11)–(13)) the following problem is posed: if X is an orientable topological n-manifold, what is the set of integers which may be obtained as the degree of(f.i) where f is a G-symmetric map? The degree of(f.i) is called the James number of f. If G = ∑n(G = Zn) a G-symmetric map will be called a symmetric map (a cyclic map). If X = Sn, the n-sphere, this problem has been studied in ((6)–(8), (11)–(13))

scholarly journals Cyclic Contractions on -Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
E. Karapınar ◽  
A. Yıldız-Ulus ◽  
İ. M. Erhan
Keyword(s):  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Integral Type ◽  
Cyclic Maps ◽  
Cyclic Contractions

Conditions for existence and uniqueness of fixed points of two types of cyclic contractions defined on -metric spaces are established and some illustrative examples are given. In addition, cyclic maps satisfying integral type contractive conditions are presented as applications.

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