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 .