Fixed point of discrete dynamical system of Lotka Volterra model

Fixed point theorem is one of the theories in mathematics that has make many proofs been in existence. Lotka-Volterra model is a widely used pair of first-order nonlinear differential equations used to interpret the dynamics of two species that is a predator and a prey. The paper employs the contraction mapping and the Banach Fixed point theory on the Discrete Dynamical type of the Lotka-Volterra to see the outcome of its behavior.The Banach Fixed Theoryis used in determining the fixed point of discrete dynamical system of Lotka Volterra model.The results shows that the solutions of Lotka Volterra Model are the fixed points the of Model. Also, the outcome of contraction mapping and Banach fixed point theory shows that the fixed points serving as the limiting behavior of Lotka Volterra is continuous and convergent.