Behavior of Various Repetitive Methods in Approaching Solutions for Complex Transformations

By: PoesÃa

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Paperback | 17 January 2025

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202 Pages

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

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