Abstract metric spaces and Sehgal-Guseman-type theorems
Abstract
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 Radenovie and Kadelburg [S. Radenovie, 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.
Keywords:
Symmetric spaces / Normal and non-normal cone / Common fixed point / Associated symmetric space / Abstract (cone) metric spaceSource:
Computers & Mathematics With Applications, 2010, 60, 3, 865-872Publisher:
- Pergamon-Elsevier Science Ltd, Oxford
DOI: 10.1016/j.camwa.2010.05.033
ISSN: 0898-1221
WoS: 000280935400044
Scopus: 2-s2.0-77955425099
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Institution/Community
Mašinski fakultetTY - JOUR AU - Pavlović, Mirjana AU - Radenović, Stojan AU - Radojević, Slobodan PY - 2010 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1102 AB - 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 Radenovie and Kadelburg [S. Radenovie, 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. PB - Pergamon-Elsevier Science Ltd, Oxford T2 - Computers & Mathematics With Applications T1 - Abstract metric spaces and Sehgal-Guseman-type theorems EP - 872 IS - 3 SP - 865 VL - 60 DO - 10.1016/j.camwa.2010.05.033 ER -
@article{ author = "Pavlović, Mirjana and Radenović, Stojan and Radojević, Slobodan", year = "2010", abstract = "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 Radenovie and Kadelburg [S. Radenovie, 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.", publisher = "Pergamon-Elsevier Science Ltd, Oxford", journal = "Computers & Mathematics With Applications", title = "Abstract metric spaces and Sehgal-Guseman-type theorems", pages = "872-865", number = "3", volume = "60", doi = "10.1016/j.camwa.2010.05.033" }
Pavlović, M., Radenović, S.,& Radojević, S.. (2010). Abstract metric spaces and Sehgal-Guseman-type theorems. in Computers & Mathematics With Applications Pergamon-Elsevier Science Ltd, Oxford., 60(3), 865-872. https://doi.org/10.1016/j.camwa.2010.05.033
Pavlović M, Radenović S, Radojević S. Abstract metric spaces and Sehgal-Guseman-type theorems. in Computers & Mathematics With Applications. 2010;60(3):865-872. doi:10.1016/j.camwa.2010.05.033 .
Pavlović, Mirjana, Radenović, Stojan, Radojević, Slobodan, "Abstract metric spaces and Sehgal-Guseman-type theorems" in Computers & Mathematics With Applications, 60, no. 3 (2010):865-872, https://doi.org/10.1016/j.camwa.2010.05.033 . .