Iterative and approximate solutions of general parameter dependent nonlinear operator equations in Hilbert spaces

Iterative solutions of a general nonlinear operator equation of the form Ax + λTx = f, where A and T are in general nonlinear operators in an appropriate space, have not been developed so far. In this paper, the three well-known Banach, Mann, and Ishikawa iteration processes are used to find solutions of this equation in the Hilbert space case. An error estimate in each case is given. The established results generalize many of the known results in literature.