A Regular Lindelof Semimetric Space which has no Countable Network

1970 ◽  
Vol 26 (2) ◽  
pp. 361 ◽  
Author(s):  
E. S. Berney
Keyword(s):  
Semimetric Space

scholarly journals Fixed point theorems for contractions in semicomplete semimetric spaces

2018 ◽  
Vol 34 (2) ◽  
pp. 269-275
Author(s):  
TOMONARI SUZUKI ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Semimetric Space ◽  
Semimetric Spaces

We introduce the concept of semicompleteness on semimetric space, which is weaker than completeness. We prove fixed point theorems for contractions in semicomplete semimetric spaces. Also, we generalize JachymskiMatkowski-Swia¸ tkowski’s fixed point theorem in semimetric spaces.

scholarly journals Subordinate Semimetric Spaces and Fixed Point Theorems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
José Villa-Morales
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Generalized Metric Space ◽  
Generalized Metric ◽  
Semimetric Space ◽  
Semimetric Spaces ◽  
Matkowski’S Fixed Point Theorem

We introduce the concept of subordinate semimetric space. Such notion includes the concept of RS-space introduced by Roldán and Shahzad; therefore the concepts of Branciari’s generalized metric space and Jleli and Samet’s generalized metric space are particular cases. For such spaces we prove a version of Matkowski’s fixed point theorem, and introducing the concept of q-contraction we get a fixed point theorem of Kannan-Ćirić type. Moreover, using such result we characterize complete subordinate semimetric spaces.

scholarly journals Superoptimal Rate of Convergence in Nonparametric Estimation for Functional Valued Processes

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Christophe Chesneau ◽  
Bertrand Maillot
Keyword(s):  
Rate Of Convergence ◽  
Nonparametric Estimation ◽  
Continuous Time ◽  
Regression Function ◽  
Mean Square ◽  
Semimetric Space ◽  
Mean Square Convergence ◽  
The Mean ◽  
Continuous Time Processes

We consider the nonparametric estimation of the generalised regression function for continuous time processes with irregular paths when the regressor takes values in a semimetric space. We establish the mean-square convergence of our estimator with the same superoptimal rate as when the regressor is real valued.

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