Comparative Study of Convergence of Sequence of Functions in a Banach Space

Sampson Akuoko Opoku, Siba Mohammed Abubakar


We discuss four types of convergence of sequence of functions in a Banach space. The types of convergence considered include pointwise, uniform, strong and weak convergence. It is shown that uniform convergence implies the pointwise convergence and the strong Convergence implied the weak convergence. We also show how basic analysis concepts are used in proving advanced concepts and also provide an alternative description of the exponential function.


strong; weak; uniform; pointwise convergence.

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