Complex analysis in Banach spaces constitutes a robust framework in which classical methods of complex function theory are generalised to infinite dimensions. This field explores holomorphic functions ...

The principal reference for this syllabus is: [1] J.K. Hunter and B. Nachtergaele, Applied Analysis. With the exception of the topics from advanced calculus, a question may appear on the exam if and ...

Fixed point theory is a central topic in functional analysis that examines conditions under which a mapping in a Banach space admits points that remain invariant under the transformation. Particularly ...