Basic theory and applications of probabilistic metric spaces. I

DOI10.1007/BF02456008zbMath0731.54023OpenAlexW4252683378MaRDI QIDQ808022

Shi Sheng Zhang

Publication date: 1988

Published in: Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/15664

zbMATH Keywords

fixed point theorylinear operatorprobabilistic metric spacesMenger PM-spacesPM-spaceprobabilistic normed linear spacesprobabilistically bounded sets

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Fixed-point and coincidence theorems (topological aspects) (54H25) Other ``topological linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) (46A19) Probabilistic metric spaces (54E70)

Related Items (8)

New version of KKM theorem in probabilistic metric spaces with applications ⋮ Probabilistic norm of linear operators on PN space ⋮ On probabilistic norms of linear operators and spaces of operators ⋮ Basic theory and applications of probabilistic metric spaces. II ⋮ A representation theorem for fuzzy pseudometrics ⋮ Fixed point theorems in generating spaces of quasi-norm family and applications ⋮ Probabilistic norm of operators and resonance theorems ⋮ On the isometric isomorphism of probabilistic metric spaces

Cites Work

• The metrization of statistical metric spaces
• Multi-valued contraction mappings
• On the theory of probabilistic metric spaces with applications
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