We prove some generalizations of the first Fredholm theorem for Hammerstein operator equations in Banach spaces and study the number of their solutions using a projection like method.The linear part is assumed to be either selfadjoint or nonseladjoint while the nonlinearities are such that the corresponding map is (pseudo) A-proper. In particular, the nonlinearities can be either of monotone ty...

A plethora of sufficient convergence criteria has been provided for single-step iterative methods to solve Banach space valued operator equations. However, an interesting question remains unanswered: is it possible provide unified methods, which are weaker than earlier ones without additional hypotheses? The answer yes. In particular, we only one criterion suitable methods. Moreover, also give ...

In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: [Formula: see text] where [Formula: see text]; [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] where [Formu...

In a recent paper [3], Y. Cao and Y. Xu established the Galerkin method for weakly singular Fredholm integral equations that preserves the singularity of the solution. Their Galerkin method provides a numerical solution that is a linear combination of a certain class of basis functions which includes elements that reflect the singularity of the solution. The purpose of this paper is to extend t...