Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 4 6 2016 11 5 New Approach of F-Contraction Involving Fixed Point on a Closed Ball 159 163 EN Aftab Hussain Department of Mathematics, International Islamic University, H-10, Islam-abad, Pakistan TJANT2016462 10.12691/tjant-4-6-2 2016 7 23 2016 10 6 2016 11 3 The article is written with a view to introducing the new idea of F-contraction on a closed ball and have new theorems in a complete metric space. That is why this outcome becomes useful for the contraction of the mapping on a closed ball instead of the whole space. At the same time, some comparative examples are constructed which establish the superiority of our results. It can be stated that the results that have come into being give proof of extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.