scholarly journals Functionally σ-discrete mappings and a generalization of Banach's theorem

2015 ◽  
Vol 189 ◽  
pp. 92-106 ◽  
Author(s):  
Olena Karlova
Keyword(s):  
Banach's Theorem

scholarly journals On the PropertyN-1

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Stanisław Kowalczyk ◽  
Małgorzata Turowska
Keyword(s):  
Continuous Function ◽  
Lebesgue Measure ◽  
Continuous Functions ◽  
Approximate Derivative ◽  
Banach's Theorem ◽  
Full Lebesgue Measure

We construct a continuous functionf:[0,1]→Rsuch thatfpossessesN-1-property, butfdoes not have approximate derivative on a set of full Lebesgue measure. This shows that Banach’s Theorem concerning differentiability of continuous functions with Lusin’s property(N)does not hold forN-1-property. Some relevant properties are presented.

scholarly journals Some fixed point theorems

1992 ◽  
Vol 53 (3) ◽  
pp. 304-312 ◽  
Author(s):  
P. V. Subrahmanyam ◽  
I. L. Reilly
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Unique Fixed Point ◽  
Complete Metric Space ◽  
Contraction Principle ◽  
Carry Over ◽  
Banach's Theorem ◽  
Banach’S Contraction Principle

AbstractBanach's contraction principle guarantees the existence of a unique fixed point for any contractive selfmapping of a complete metric space. This paper considers generalizations of the completeness of the space and of the contractiveness of the mapping and shows that some recent extensions of Banach's theorem carry over to spaces whose topologies are generated by families of quasi-pseudometrics.

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