Abstract metric spaces and Sehgal–Guseman-type theorems

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.