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

Faik Gürsoy

We study the convergence analysis of a Picard-S iterative method for a particular class of weakcontraction 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 \[ x(t)=F\bigg(r,x(t),ıt_{a_1}^{t_1}\dotsıt_{a_m}^{t_m}K(t,s,x(s))ds,ıt_{a_1}^{b_1}\dotsıt_{a_m}^{b_m}H(t,s,x(s))ds\bigg). \] Furthermore, with the help of the Picard-S iterative method, we establish a data dependence result for the solution of integral equation mentioned above.