Fixed point theory in probabilistic metric spaces / by Olga Hadžić and Endre Pap.

Format:

Book

Author/Creator:

Hadžić, Olga.

Contributor:

Pap, Endre.

Anne and Joseph Trachtman Memorial Book Fund.

Series:

Mathematics and its applications (Kluwer Academic Publishers) ; v. 536.

Mathematics and its applications ; v. 536

Language:

English

Subjects (All):

Fixed point theory.

Metric spaces.

Probabilities.

Physical Description:

ix, 273 pages ; 25 cm.

Place of Publication:

Dordrecht ; Boston : Kluwer Academic, [2001]

Contents:

1 Triangular norms 1

1.1 Triangular norms and conorms 1

1.2 Properties of t-norms 5

1.3 Ordinal sums 10

1.4 Representation of continuous t-norms 13

1.4.1 Pseudo-inverse 13

1.4.2 Additive generators 15

1.4.3 Multiplicative generators 19

1.4.4 Isomorphism of continuous Archimedean t-norms with either T[subscript P] or T[subscript L] 21

1.4.5 General continuous t-norms 22

1.5 t-norms with left-continuous diagonals 24

1.6 Triangular norms of H-type 26

1.7 Comparison of t-norms 29

1.7.1 Comparison of continuous Archimedean t-norms 29

1.7.2 Comparison of continuous t-norms 33

1.7.3 Domination of t-norms 35

1.8 Countable extension of t-norms 38

2 Probabilistic metric spaces 47

2.1 Copulas and triangle functions 47

2.1.1 Copulas 47

2.1.2 Triangle functions 50

2.2 Definitions of probabilistic metric spaces 53

2.3 Some classes of probabilistic metric spaces 55

2.3.1 Menger and Wald spaces 56

2.3.2 Transformation-generated spaces 59

2.3.3 E-processes and Markov chains 60

2.4 Topology, uniformity, metrics and semi-metrics on probabilistic metric spaces 62

2.5 Random normed and para-normed spaces 65

2.6 Fuzzy metric spaces 70

2.7 Functions of non-compactness 75

2.8 Probabilistic metric spaces related to decomposable measure 85

2.8.1 Decomposable measures 85

2.8.2 Related probabilistic metric spaces 91

3 Probabilistic B-contraction principles for single-valued mappings 95

3.1 Probabilistic B-contraction principles 96

3.2 Two special classes of probabilistic q-contractions 111

3.3 Generalizations of probabilistic B-contractions principles for single-valued mappings 116

3.4 Fixed point theorems of Caristi's type 132

3.5 Common fixed point theorems 140

4 Probabilistic B-contraction principles for multi-valued mappings 155

4.1 Multi-valued contractions of Mihet's type 155

4.2 Multi-valued probabilistic [Psi]-contractions 158

4.3 Probabilistic Nadler q-contraction 162

4.4 A fixed point theorem of Itoh's type 168

4.5 Fixed point theorems in probabilistic metric spaces with convex structures 174

4.6 A common fixed point theorem for sequence of mappings 181

5 Hicks' contraction principle 185

5.1 Hicks' contraction principle for single-valued mappings 185

5.2 Multi-valued generalizations of Hicks' contraction principle 195

6 Fixed point theorems in topological vector spaces and applications to random normed spaces 205

6.1 Tychonoff's and Browder's fixed point theorems 206

6.2 Admissible subsets of topological vector spaces and their application on the fixed point theory 213

6.3 Fixed point theorems of Krasnoselski's type 225

6.4 Continuous dependence of the fixed points on the parameters of ([alpha], g)-condensing mappings 233

6.5 A degree theory in topological vector spaces 239.

Notes:

Includes bibliographical references (pages 245-267) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Anne and Joseph Trachtman Memorial Book Fund.

ISBN:

1402001290

OCLC:

48176824