Foundations of the Fredholm Alternative Theorem, Equicontinuous Operators and Completely Continuous Operators

Abstract

The Fredholm Alternative Theorem gives the notion of bounded and continuous operator which makes a family F of elements of C[a, b] bounded and equicontinuous. A continuous operator of finite rank is completely continuous but every continuous operator is not completely continuous operator. Keywords: Arzela-Ascoli's theorem; completely continuous; equicontinuous and Fredholm alternative theorem DOI: http://dx.doi.org/10.3126/bibechana.v8i0.5700 BIBECHANA 2012; 8: 127-130