On eigenvalues and surjectivity using fixed points

Anoop. S. K.
Research Scholar, P. G. Dept. and Research Centre in Mathematics, Payyanur College, Payyanur, Kannur, Kerala, India.
K. T. Ravindran
Reader, P. G. Dept. and Research Centre in Mathematics, Payyanur College, Payyanur,
Kannur, Kerala, India.

\(^{1}\)Corresponding Author: anooperul@rediffmail.com

Copyright © 2009 Anoop. S. K. , K. T. Ravindran. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2009.

Abstract

Here first we will prove the existence of fixed points for a weakly continuous, strictly quasi bounded operator on a reflexive Banach space and a completely continuous, strictly quasi bounded operator on any normed linear space. Using these results we can deduce the existence of eigen values and surjectivity of quasi bounded operator in similar situations.

Keywords:

Reflexive banach space, weakly continuous functions, completely continuous functions, quasi bounded functions, strictly quasi bounded functions.