Existence of Solutions of Operator Equations with Applications: Lahore University of Management Sciences, 2012

Nazir, Talat; Abbas, Mujahid

ISBN 10: 3659242519 / ISBN 13: 9783659242519

Published by LAP LAMBERT Academic Publishing, 2012

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Bibliographic Details

• Title: Existence of Solutions of Operator Equations with Applications: Lahore University of Management Sciences, 2012
• Publisher: LAP LAMBERT Academic Publishing
• Publication Date: 2012
• Language: English
• ISBN 10: 3659242519
• ISBN 13: 9783659242519
• Binding: Soft cover
• Condition: New

About this title

Synopsis

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 the existence of solutions to operator equations, including ordinary differential equations, partial differential equations and integral equations. This principle has been generalized in many directions.

About the Author

Department of Mathematics, Lahore University of Management Sciences, Pakistan.