eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2015-06-28 3 2 70 74 10.12691/tjant-3-2-7 TJANT2015327 article Krishna Patel krishnappatel10@gmail.com 1 G M Deheri 1 Department of Mathematics, Sardar Patel University, Anand, Gujarat, India Results dealing with a Fixed Point for a map need not be continuous on a metric space, which improves a famous classical result, has been presented here, wherein the convergence aspect is duly addressed. This paper aims to present some fixed point theorems on metric spaces. It can be easily observed that these are significant improvement of some of the well-known classical result dealing with the generalization of Banach fixed point theorem. Further, here the rate of convergence aspects is duly taken care of. http://pubs.sciepub.com/tjant/3/2/7/tjant-3-2-7.pdf fixed point metric space sequential convergent subsequential convergent uniqueness