cyclic maps
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Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1060
Author(s):  
Miroslav Hristov ◽  
Atanas Ilchev ◽  
Boyan Zlatanov

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.


2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
M. De la Sen

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.


2012 ◽  
Vol 55 (3) ◽  
pp. 523-536 ◽  
Author(s):  
Norio Iwase ◽  
Mamoru Mimura ◽  
Nobuyuki Oda ◽  
Yeon Soo Yoon

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.


2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
E. Karapınar ◽  
A. Yıldız-Ulus ◽  
İ. M. Erhan

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.


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

2004 ◽  
Vol 249 (1) ◽  
pp. 113-124 ◽  
Author(s):  
Gregory Lupton ◽  
Samuel Bruce Smith

1990 ◽  
Vol 42 (5) ◽  
pp. 856-868 ◽  
Author(s):  
Nobuyuki Oda

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].


1984 ◽  
Vol 27 (1) ◽  
pp. 78-86 ◽  
Author(s):  
K. L. Lim

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.


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

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