scholarly journals Necessary and sufficient conditions for common fixed point theorems in fuzzy metric space

2009 ◽  
Vol 42 (4) ◽  
Author(s):  
D. O’Regan ◽  
M. Abbas
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Fuzzy Metric Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Common Fixed Point Theorems

AbstractThe aim of this paper is to provide a necessary and sufficient condition for the existence of a common fixed point of three maps

scholarly journals Common Fixed Point Theorems in a New Fuzzy Metric Space

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Weiquan Zhang ◽  
Dong Qiu ◽  
Zhifeng Li ◽  
Gangqiang Xiong
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Positive Real Number ◽  
Fuzzy Metric Space ◽  
Positive Real ◽  
Fuzzy Metric ◽  
Contraction Condition ◽  
Common Fixed Point Theorems

We generalize the Hausdorff fuzzy metric in the sense of Rodríguez-López and Romaguera, and we introduce a newM∞-fuzzy metric, whereM∞-fuzzy metric can be thought of as the degree of nearness between two fuzzy sets with respect to any positive real number. Moreover, underϕ-contraction condition, in the fuzzy metric space, we give some common fixed point theorems for fuzzy mappings.

scholarly journals Orbital continuity and fixed points

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3495-3499 ◽  
Author(s):  
Abhijit Pant ◽  
R.P. Pant
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Metric Space ◽  
Complete Metric Space ◽  
Sufficient Condition ◽  
Point Property ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Type Contraction

The aim of the present paper is to show the significance of the concept of orbital continuity introduced by Ciric. We prove that orbital continuity of a pair of R-weak commuting self-mappings of type Af or of type A1 of a complete metric space is equivalent to fixed point property under Jungck type contraction. We also establish a situation in which orbital continuity is a necessary and sufficient condition for the existence of a common fixed point of a pair of mappings yet the mappings are necessarily discontinuous at the fixed point.

scholarly journals Some fixed point theorems in fuzzy metric space

2008 ◽  
Vol 39 (4) ◽  
pp. 309-316 ◽  
Author(s):  
Urmila Mishra ◽  
Abhay Sharad Ranadive ◽  
Dhananjay Gopal
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fuzzy Metric Space ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Reciprocal Continuity ◽  
Common Fixed Point Theorems

In this paper we prove common fixed point theorems in fuzzy metric spaces employing the notion of reciprocal continuity. Moreover we have to show that in the context of reciprocal continuity the notion of compatibility and semi-compatibility of maps becomes equivalent. Our result improves recent results of Singh & Jain [13] in the sense that all maps involved in the theorems are discontinuous even at common fixed point.

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