A new approach to fuzzy partial metric spaces

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GÜNER E., AYGÜN H.

Hacettepe Journal of Mathematics and Statistics, cilt.51, sa.6, ss.1563-1576, 2022 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 6
  • Basım Tarihi: 2022
  • Doi Numarası: 10.15672/hujms.1115381
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1563-1576
  • Anahtar Kelimeler: partial metric, fuzzy metric, topology, fuzzifying topology, fixed point theorem
  • Kocaeli Üniversitesi Adresli: Evet

Özet

© 2022, Hacettepe University. All rights reserved.In this study, we aim to introduce the notion of fuzzy partial metric spaces which is a generalization of crisp partial metric spaces in the fuzzifying view with the distance between ordinary points. For this aim, we first present the concept of fuzzy partial metric spaces by considering the distance as non-negative, upper semi-continuous, normal and convex fuzzy numbers by giving examples. We obtain some useful inequalities under some restrictions in fuzzy partial metric spaces. Then we discuss the relationships with the other metric structures and we point out Banach’s fixed point theorem as an application of the proposed properties and relations. Finally, we show that fuzzy partial metric spaces induce some α-level topology, Lowen fuzzy topology, and fuzzifying topology.