International Journal of Pure and Applied Mathematics Volume 92 No. 3 2014, 381-388 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v92i3.6 P A ijpam.eu FIXED POINT THEOREMS FOR A SELF MAP ON COMPACT METRIC SPACE Pushpendra Semwal 1 § , R.C. Dimri 2 1,2 Department of Mathematics H.N.B. Garhwal University Srinagar Garhwal, INDIA Abstract: In this paper we investigate certain conditions that imply the existence of fixed points for contraction mappings in the setting of compact metric spaces. As a result we obtain generalized results by unifying some recent related fixed point theorems on the topic. AMS Subject Classification: 47H10, 46B20, 54H25 Key Words: compact metric space, fixed point, self map 1. Introduction and Preliminaries Fixed point theory plays a fundamental role in solving functional equations [1] arising in several areas of mathematics and other related disciplines as well. The Banach contraction principle is a key principle [2] that made a remarkable progress towards the development of metric fixed point theory. Banach’s result is the origin and antecedents results by the fact that he not only proved the existence and uniqueness of a fixed point of a contraction, but also showed how to evaluate this point. After this celebrated result [2], a number of authors have observed various other types of contraction mappings and proved related fixed point point theorems such as Kannan [3], Reich [4], Hardy and Rogers [5], Ciric [6-8], Zamfirescu [9], Arshad et al [10]. By following this trend Suzuki recently proved the following fixed point theorems: Received: October 23, 2013 c  2014 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author