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

Authors

  • Sampson Akuoko Opoku Mathematics Department, KNUST- Kumasi, Ghana
  • Siba Mohammed Abubakar P. O. Box NU 26, Nsuta

Keywords:

strong, weak, uniform, pointwise convergence.

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.

References

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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

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

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Published

2017-03-16

How to Cite

Opoku, S. A., & Abubakar, S. M. (2017). Comparative Study of Convergence of Sequence of Functions in a Banach Space. International Journal of Sciences: Basic and Applied Research (IJSBAR), 32(2), 43–53. Retrieved from https://www.gssrr.org/index.php/JournalOfBasicAndApplied/article/view/6297

Issue

Vol. 32 No. 2 (2017)

Section

Articles

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