Convergence Comparison of two Schemes for Common Fixed Points with an Application

Some cases of common fixed point theory for classes of generalized nonexpansive maps are studied. Also, we show that the Picard-Mann scheme can be employed to approximate the unique solution of a mixed-type Volterra-Fredholm functional nonlinear integral equation.

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 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(t, x(t), ?t1,a1... ?tm,am K(t,s,x(s))ds, ?b1,a1...?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.

On Nonlinear Second Order Volterra-Fredholm Functional Integrodifferential Equation with Nonlocal Condition in Banach Spaces

Our purpose in this paper is to study the existence of solution of nonlinear second order mixed functional integrodifferential equation with nonlocal condition in Banach space by employing two different techniques namely the Darbo-Sadovskii's fixed point theorem with Hausdorff's measure of noncompactness and the Leray Schauder Alternative.

Applications of Normal S-Iterative Method to a Nonlinear Integral Equation

It has been shown that a normal S-iterative method converges to the solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. Furthermore, a data dependence result for the solution of this integral equation has been proven.

Global existence for abstract nonlinear Volterra–Fredholm functional integrodifferential equation

In the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra–Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray–Schauder alternative and rely on a priori bounds of solution.