Behavior of Various Repetitive Methods in Approaching Solutions for Complex Transformations

<p>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 Sˆ defined on Y into itself is called a fixed point or invari- ant point of that transformation Sˆ. Denote Fix(Sˆ) as set of all fixed points of mapping Sˆ Fix(Sˆ) = {t ? Y : Sˆ(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 Sˆ defined on the space Y having one or more fixed points under certain con- ditions on the mapping ace Y . </p>