• ON A MAP OF XIA ET.AL AND SOME FIXED POINT THEOREMS FOR A CLASS OF CONTRACTIVE MAPPINGS IN G-DISLOCATED METRIC SPACES

Abstract

In Xia et.al  [Common fixed points for two self-mappings on symmetric sets and complete metric spaces, Advances in Mathematics, vol. 36, no. 4, pp. 415–420, 2007.], the following map is introduced: Let , let , and , satisfy the following: (i) if , then there exist , such that ; (ii) if , then there exists , such that . The authors use these maps to prove the following fixed point result: Let be a complete metric space, and let be continuous mappings, and for all such that

, or ,

then,  have a unique common fixed point. In the present paper we define an analogous map in the setting of G-dislocated metric spaces and use it to obtain fixed point theorems.