Abstract
Gregori and Romaguera introduced, in 2004, the notion of a KM-fuzzy quasi-metric space as a natural asymmetric generalization of the concept of fuzzy metric space in the sense of Kramosil and Michalek. Ever since, various authors have discussed several aspects of such spaces, including their topological and (quasi-)metric properties as well as their connections with domain theory and their relationship with other fuzzy structures. In particular, the development of the fixed point theory for these spaces and other related ones, such as fuzzy partial metric spaces, has received remarkable attention in the last 15 years. Continuing this line of research, we here establish general fixed point theorems for left and right complete Hausdorff KM-fuzzy quasi-metric spaces, which are applied to deduce characterizations of these distinguished kinds of fuzzy quasi-metric completeness. Our approach, which mixes conditions of Suzuki-type with contractions of α−ϕ-type in the well-known proposal of Samet et al., allows us to extend and improve some recent theorems on complete fuzzy metric spaces. The obtained results are accompanied by illustrative and clarifying examples.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference52 articles.
1. Fuzzy quasi-metric spaces;Gregori;Appl. Gen. Topol.,2004
2. Cho, Y.J., Grabiec, M., and Radu, V. (2006). On Nonsymmetric Topologial and Probabilistic Structures, Nova Science Publishers, Inc.
3. Fuzzy metrics and statistical metric spaces;Kramosil;Kybernetika,1975
4. On some results in fuzzy metric spaces;George;Fuzzy Sets Syst.,1994
5. On some results of analysis of fuzzy metric spaces;George;Fuzzy Sets Syst.,1997