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

Sampson Akuoko Opoku, Siba Mohammed Abubakar

Abstract


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.

 


Keywords


strong; weak; uniform; pointwise convergence.

References


RUDIN, W., Principles of Mathematical Analysis, 3rd edition (New York: McGraw-Hill), 1976.

KREYSZIG, E., Introductory functional Analysis With Applications (W.C.Library, Ed.) John Wiley and Sons, Inc., 1978, pp.189-190,

WHEEDEN, R.L., & ZYGMOND, A., Measure and Integral,(S.Kobayashi,Ed.) Marcel Dekker, Inc. New York and Basel, 1977.

WICKLESS,W.J. , A Graduate Course in Abstract Algebra.,(E.J.Taft, Ed.) Marcel Dekker, Inc New York and Basel, 2004.

K. ATKINSON & W. HAN, Theoretical Numerical Analysis – A Functional Analysis Framework, ( J. E. Marsden, Ed ) Springer-Verlag New York, Inc. , 2001,pp. 72

L. DEBNATH & P. MIKUSINSKI, Introduction to Hilbert Spaces with Applications, (2ndEd) San Diego: Academic Press , 1999,pp.19-20


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