Behavior of Various Repetitive Methods in Approaching Solutions for Complex Transformations

The most of the important solution of nonlinear problems of applied mathe- matics can be converted to finding the solutions of nonlinear operator equa- tions (e.g. a system of differential and integral equations, variational inequal- ities, image recovery, split feasibility problems, signal processing, control the- ory, convex optimization, approximation theory, convex feasibility, monotone inequality and differential inclusions etc.) which can be formulated in terms of fixed point problems (FPP). A point of a set Y which is invariant under any transformation S^ defined on Y into itself is called a fixed point or invari- ant point of that transformation S^. Denote Fix(S^) as set of all fixed points of mapping S^, Fix(S^) = {t ? Y: S^(t) = t}, throughout in this thesis and assume that it is nonempty. The fixed point theorem is a statement that asserts that a self mapping S^ defined on the space Y having one or more fixed points under certain con- ditions on the mapping ace Y .