scholarly journals Common Fixed Point Theorems for Compatible Maps in Generalized Fuzzy Metric Spaces

2021 ◽  
pp. 88-96
Author(s):  
M. Jeyaraman ◽  
S. Sowndrarajan ◽  
A. Ramachandran
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Compatible Maps ◽  
Weakly Compatible Maps ◽  
Implicit Relation ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Weakly Compatible ◽  
Common Fixed Point Theorems

In this paper, we consider generalized fuzzy metric spaces and provide existence and uniqueness fixed point results. First, we use compatible maps of type (β) to prove fixed point results, then we introduce weakly compatible maps to approximate common fixed point results by using an implicit relation.

scholarly journals Some Common Fixed Point Theorems in Generalized Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Manoj Kumar ◽  
Pankaj Kumar ◽  
Sanjay Kumar
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Compatible Maps ◽  
Weakly Compatible Maps ◽  
Generalized Metric Spaces ◽  
Weakly Compatible ◽  
Common Fixed Point Theorems ◽  
Common Limit Range Property

First we prove common fixed point theorems for weakly compatible maps which generalize the results of Chen (2012). Secondly, we prove common fixed point theorems using property E.A. along with weakly compatible maps. At the end, we prove common fixed point theorems using common limit range property (CLR property) along with weakly compatible maps.

scholarly journals Weakly compatible maps in fuzzy metric spaces

1970 ◽  
Vol 7 (1) ◽  
pp. 28-37
Author(s):  
M Rangamma ◽  
G Mallikarjun Reddy ◽  
P Srikanth Rao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Compatible Maps ◽  
Weakly Compatible Maps ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Weakly Compatible ◽  
Commuting Maps ◽  
Reciprocal Continuity

In this paper, we prove common fixed point theorems for six self maps by using weakly compatibility, without appeal to continuity in fuzzy metric space. Our results extend, generalized several fixed point theorems on metric and fuzzy metric spaces.   Mathematics subject classification: 47H10, 54H25. Keywords : Compatible maps, R-weakly commuting maps, Reciprocal continuity, weakly compatible. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5419 KUSET 2011; 7(1): 28-37

scholarly journals Weakly compatible maps in complex valued metric spaces and an application to solve Urysohn integral equation

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2695-2709
Author(s):  
Manoj Kumar ◽  
Pankaj Kumar ◽  
Sanjay Kumar ◽  
Serkan Araci
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Compatible Maps ◽  
Weakly Compatible Maps ◽  
Weakly Compatible ◽  
Urysohn Integral Equations ◽  
Complex Valued ◽  
Common Fixed Point Theorems

In this paper, we prove common fixed point theorems for a pair of mappings satisfying rational inequality. Also, we prove common fixed point theorems for weakly compatible maps, weakly compatible along with (CLR) and E.A. properties that generalizes the results of Sintunavarat et al. [15]. Further, we apply our results to find the solution of Urysohn integral equations x(t) = ?b,a K1(t,s,x(s))ds + g(t), x(t) = ?b,a K2(t,s,x(s))ds + h(t), where t ? [a,b]? R,x,g,h ? X and K1,K2: [a,b] x [a,b] x Rn ? Rn.

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