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 Fixed Points of Geraghty-Type Mappings in Various Generalized Metric Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dušan Ðukić ◽  
Zoran Kadelburg ◽  
Stojan Radenović
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Partial Metric ◽  
Generalized Metric Spaces ◽  
Generalized Metric ◽  
Partial Metric Spaces ◽  
Type Spaces

Fixed point theorems for mappings satisfying Geraghty-type contractive conditions are proved in the frame of partial metric spaces, ordered partial metric spaces, and metric-type spaces. Examples are given showing that these results are proper extensions of the existing ones.

Fixed point theorems for a system of transformations in generalized metric spaces

2015 ◽  
Vol 08 (04) ◽  
pp. 1550068 ◽  
Author(s):  
Stefan Czerwik ◽  
Krzysztof Król
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fixed Points ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Banach Fixed Point Theorem ◽  
Generalized Metric Spaces ◽  
Generalized Metric

In this paper we present the results on the existence of fixed points of system of mappings in generalized metric spaces generalizing the result of Diaz and Margolis. Also the “local fixed point theorems” of a system of such mappings both in generalized and ordinary metric spaces are stated. Banach fixed point theorem and many others are consequences of our results.

scholarly journals Fixed Points Results forα-Admissible Mapping of Integral Type on Generalized Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Erdal Karapınar
Keyword(s):  
Fixed Points ◽  
Metric Spaces ◽  
Integral Type ◽  
Generalized Metric Spaces ◽  
Contractive Mappings ◽  
Admissible Mapping ◽  
Generalized Metric

We introduce generalized(α,ψ)-contractive mappings of integral type in the context of generalized metric spaces. The results of this paper generalize and improve several results on the topic in literature.

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