The Generic Stability of Fixed Points for Upper Semicontinuous Mappings in Hyperconvex Metric Spaces

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

Abstract and Applied Analysis ◽

10.1155/2011/561245 ◽

2011 ◽

Vol 2011 ◽

pp. 1-13 ◽

Cited By ~ 22

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.

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A note on common fixed points for ( ψ , α , β ) -weakly contractive mappings in generalized metric spaces

Fixed Point Theory and Applications ◽

10.1186/1687-1812-2013-287 ◽

2013 ◽

Vol 2013 (1) ◽

Cited By ~ 10

Author(s):

Nurcan Bilgili ◽

Erdal Karapınar ◽

Duran Turkoglu

Keyword(s):

Fixed Points ◽

Metric Spaces ◽

Common Fixed Points ◽

Generalized Metric Spaces ◽

Contractive Mappings ◽

Generalized Metric ◽

Weakly Contractive

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RANDOM COINCIDENCE AND FIXED POINTS FOR WEAKLY COMPATIBLE MAPPINGS IN CONVEX METRIC SPACES

Asian-European Journal of Mathematics ◽

10.1142/s1793557109000145 ◽

2009 ◽

Vol 02 (02) ◽

pp. 171-182 ◽

Cited By ~ 2

Author(s):

Izmat Beg ◽

Adnan Jahangir ◽

Akbar Azam

Keyword(s):

Fixed Points ◽

Metric Spaces ◽

Weakly Compatible Mappings ◽

Compatible Mappings ◽

Coincidence Points ◽

Random Coincidence ◽

Complete Metric Spaces ◽

Random Fixed Points ◽

Weakly Compatible ◽

Convex Metric Spaces

Some new theorems on random coincidence points and random fixed points for weakly compatible mappings in convex separable complete metric spaces have been established. These results generalize some recent well known comparable results in the literature.

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