A Picard-S Iterative Method for Approximating Fixed Point of Weak-Contraction Mappings

We study the convergence analysis of a Picard-S iterative method for a particular class of weak-contraction mappings and give a data dependence result for fixed points of these mappings. Also, we show that the Picard-S iterative method can be used to approximate the unique solution of mixed type Volterra-Fredholm functional nonlinear integral equation x(t) = F(t, x(t), integral(t1)(a1) center dot center dot center dot integral(tm)(am) K(t, s, x(s))ds, integral(b1)(a1) center dot center dot center dot integral(bm)(am) H(t, s, x(s))ds,). Furthermore, with the help of the Picard-S iterative method, we establish a data dependence result for the solution of integral equation mentioned above.