Surveys in Mathematics and its Applications


ISSN 1842-6298 (electronic), 1843 - 7265 (print)
Volume 2 (2007), 123 - 143

FAMILIES OF QUASI-PSEUDO-METRICS GENERATED BY PROBABILISTIC QUASI-PSEUDO-METRIC SPACES

Mariusz T. Grabiec, Yeol Je Cho and Reza Saadati

Abstract. This paper contains a study of families of quasi-pseudo-metrics (the concept of a quasi-pseudo-metric was introduced by Wilson [22] , Albert [1] and Kelly [9]) generated by probabilistic quasi-pseudo-metric-spaces which are generalization of probabilistic metric space (PM-space shortly) [2, 3, 4, 6]. The idea of PM-spaces was introduced by Menger [11, 12], Schweizer and Sklar [18] and Serstnev [19]. Families of pseudo-metrics generated by PM-spaces and those generalizing PM-spaces have been described by Stevens [20] and Nishiure [14].

2000 Mathematics Subject Classification: 54E40.
Keywords: Families generated by PpqM-spaces; Quasi-pseudo-Menger space; Probabilistic quasi-pseudo-metric spaces (PpqM-space); Statistical quasi-metric space (SpqM-space).

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Acknowledgment. The authors would like to thank the referees and the area editor Prof. Barnabas Bede for giving useful comments and suggestions for improving the paper.

Mariusz T. Grabiec Yeol Je Cho
Department of Operation Research, Department of Mathematics and the RINS,
al. Niepodleglosci 10, Gyeongsang National University,
60-967 Poznan, Chinju 660-701,
Poland. Korea.
e-mail: m.grabiec@poczta.onet.pl e-mail: yjcho@gsnu.ac.kr


Reza Saadati
Faculty of Sciences
University of Shomal,
Amol, P.O. Box 731,
Iran.
and
Department of Mathematics and Computer Science,
Amirkabir University of Technology,
424 Hafez Avenue, Tehran 15914,
Iran.
e-mail: rsaadati@eml.cc

http://www.utgjiu.ro/math/sma