Existence of Solutions of Operator Equations with Applications
Автор:Talat Nazir and Mujahid Abbas Год: 2012 Издание:LAP Lambert Academic Publishing Страниц: 140 ISBN: 9783659242519 Various problems of a practical nature arising in physics, chemistry, biology, economy, social sciences, etc. can be modeled using a certain mathematical setup. Such models give rise to a variety of equations or a system of equations. The problems becomes more sophisticated when one deals with operator equations where the unknown object is an operator acting between two abstract spaces of different kinds. Now regarding solutions of such equations, some fundamental questions arise: Does there exist a solution? And if the answer is affirmative then it passes to the next questions: how can the solution be constructed? how many solutions are there? what is the structure of the set of all solutions? The problem of existence of a solution becomes equivalent to the problems of finding a fixed point of a certain operator. Hence results from fixed point theory can then be employed to obtain the solution of an operator equation. Banach's contraction principle is broadly applicable in proving...
