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A Picard-S iterative method for approximating fixed point of weak-contraction mappings. (English) Zbl 1465.47054
Summary: 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 \[ x (t) = F\left(t, x(t), \int^{t_1}_{a_1}\dots \int^{t_m}_{a_m} K(t,s,x(s))ds, \int^{b_1}_{a_1}\dots \int^{b_m}_{a_m} H(t,s,x(s))ds\right). \] Furthermore, with the help of the Picard-S iterative method, we establish a data dependence result for the solution of integral equation mentioned above.

MSC:
47J26 Fixed-point iterations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
45G99 Nonlinear integral equations
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