Fixed point theory in probabilistic metric spaces /
Saved in:
| Author / Creator: | Hadžić, Olga. |
|---|---|
| Imprint: | Dordrecht ; Boston : Kluwer Academic, c2001. |
| Description: | ix, 273 p. ; 25 cm. |
| Language: | English |
| Series: | Mathematics and its applications ; v. 536 Mathematics and its applications (Kluwer Academic Publishers) ; v. 536. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4661771 |
Table of Contents:
- Introduction
- 1. Triangular norms
- 1.1. Triangular norms and conorms
- 1.2. Properties of t-norms
- 1.3. Ordinal sums
- 1.4. Representation of continuous t-norms
- 1.4.1. Pseudo-inverse
- 1.4.2. Additive generators
- 1.4.3. Multiplicative generators
- 1.4.4. Isomorphism of continuous Archimedean t-norms with either T[subscript P] or T[subscript L]
- 1.4.5. General continuous t-norms
- 1.5. t-norms with left-continuous diagonals
- 1.6. Triangular norms of H-type
- 1.7. Comparison of t-norms
- 1.7.1. Comparison of continuous Archimedean t-norms
- 1.7.2. Comparison of continuous t-norms
- 1.7.3. Domination of t-norms
- 1.8. Countable extension of t-norms
- 2. Probabilistic metric spaces
- 2.1. Copulas and triangle functions
- 2.1.1. Copulas
- 2.1.2. Triangle functions
- 2.2. Definitions of probabilistic metric spaces
- 2.3. Some classes of probabilistic metric spaces
- 2.3.1. Menger and Wald spaces
- 2.3.2. Transformation-generated spaces
- 2.3.3. E-processes and Markov chains
- 2.4. Topology, uniformity, metrics and semi-metrics on probabilistic metric spaces
- 2.5. Random normed and para-normed spaces
- 2.6. Fuzzy metric spaces
- 2.7. Functions of non-compactness
- 2.8. Probabilistic metric spaces related to decomposable measure
- 2.8.1. Decomposable measures
- 2.8.2. Related probabilistic metric spaces
- 3. Probabilistic B-contraction principles for single-valued mappings
- 3.1. Probabilistic B-contraction principles
- 3.2. Two special classes of probabilistic q-contractions
- 3.3. Generalizations of probabilistic B-contractions principles for single-valued mappings
- 3.4. Fixed point theorems of Caristi's type
- 3.5. Common fixed point theorems
- 4. Probabilistic B-contraction principles for multi-valued mappings
- 4.1. Multi-valued contractions of Mihet's type
- 4.2. Multi-valued probabilistic [Psi]-contractions
- 4.3. Probabilistic Nadler q-contraction
- 4.4. A fixed point theorem of Itoh's type
- 4.5. Fixed point theorems in probabilistic metric spaces with convex structures
- 4.6. A common fixed point theorem for sequence of mappings
- 5. Hicks' contraction principle
- 5.1. Hicks' contraction principle for single-valued mappings
- 5.2. Multi-valued generalizations of Hicks' contraction principle
- 6. Fixed point theorems in topological vector spaces and applications to random normed spaces
- 6.1. Tychonoff's and Browder's fixed point theorems
- 6.2. Admissible subsets of topological vector spaces and their application on the fixed point theory
- 6.3. Fixed point theorems of Krasnoselski's type
- 6.4. Continuous dependence of the fixed points on the parameters of ([alpha], g)-condensing mappings
- 6.5. A degree theory in topological vector spaces
- Bibliography
- Index
