Abstract metric spaces and Sehgal-Guseman-type theorems

作者：Pavlovic Mirjana; Radenovic Stojan^*; Radojevic Slobodan

来源：Computers & Mathematics with Applications, 2010, 60(3): 865-872.

DOI：10.1016/j.camwa.2010.05.033

• Common fixed point
• Abstract (cone) metric space
• Normal and non-normal cone
• Symmetric spaces
• Associated symmetric space

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.

• 出版日期2010-8