𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Abstract metric spaces and Sehgal–Guseman-type theorems

✍ Scribed by Mirjana Pavlović; Stojan Radenović; Slobodan Radojević

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
312 KB
Volume
60
Category
Article
ISSN
0898-1221

No coin nor oath required. For personal study only.

✦ Synopsis

Recently, Raja and Vaezpour [P. Raja and S.M. Vaezpour, Some extensions of Banach's contraction principle in complete cone metric spaces, Fixed Point Theory Appl. 2008, 11 pages, doi:10.1155/2008/768294. Article ID 768294] proved some results for Sehgal-Guseman-type theorems in the framework of abstract (cone) metric spaces over a normal solid cone. The purpose of this paper is to present this in the framework of symmetric spaces which are associated with abstract (cone) metric spaces introduced by Radenović and Kadelburg [S. Radenović, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, ISI J. BJMA (electronic) (in press)]. Our results extend and generalize Sehgal-Guseman-type theorems from metric and abstract metric spaces to some symmetric spaces. Examples are given to illustrate the results.

📜 SIMILAR VOLUMES

Universal metric spaces and factorizatio
Universal metric spaces and factorization theorems
✍ Miroslav Husek; Stephen Watson 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 269 KB

It is shown that every continuous mapping from a metrizable space into a T0-space X can be factorized via a metrizable space of cardinality at most 2 wx. The assumption of To is essential. This solves completely a Herrlich's problem about almost coreflectivity of metrizable spaces.

Coincidence point theorems and minimizat
Coincidence point theorems and minimization theorems in fuzzy metric spaces
✍ S.S. Chang; Y.J. Cho; B.S. Lee; J.S. Jung; S.M. Kang 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 532 KB

In this paper, some new versions of coincidence point theorems and minimization theorems for single-valued and multi-valued mappings in generating spaces of the quasi-metric family are obtained. As applications, we utilize our main theorems to prove coincidence point theorems, fixed point theorems a

Generalized Probabilistic Metric Spaces
Generalized Probabilistic Metric Spaces and Fixed Point Theorems
✍ Nguyen Xuan Tan 📂 Article 📅 1986 🏛 John Wiley and Sons 🌐 English ⚖ 707 KB

Several results concerning generalized probabilistic spaces, fixed points of mappings on topological spaces are obtained and applied to yield some new theorems on fixed points for mappings on generalized probabilistic metric spaces.

Meir–Keeler-type conditions in abstract
Meir–Keeler-type conditions in abstract metric spaces
✍ Zoran Kadelburg; Stojan Radenović 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 219 KB

Various Meir-Keeler-type conditions for mappings acting in abstract metric spaces are presented and their connections are discussed. Results about associated symmetric spaces, obtained in [S. Radenović, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5