eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2022-10-30 10 3 69 75 10.12691/ajams-10-3-1 AJAMS20221031 article A New Approach to Fixed Point Theorems on a Metric Space Endowed with Graph R. Hemavathy 1 R. Om Gayathri omgayathri.r@gmail.com 2 Department of Mathematics, Queen Mary¡¯s College (Affiliated to University of Madras), Chennai, Tamil Nadu, India Department of Mathematics, Meenakshi College for Women (Affiliated to University of Madras), Chennai, Tamil Nadu, India In this paper, a new approach has been discussed to define the graph associated with the metric space and the iteration function is used to define its sub-graph. Subsequently, the fixed point theorems by Banach, Kannan, Chatterjea and Ciric are obtained using this new approach. http://pubs.sciepub.com/ajams/10/3/1/ajams-10-3-1.pdf fixed point iterated function graph sub-graph w-sequence