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 APM  Vol.5 No.9 , July 2015
A Remark on the Uniform Convergence of Some Sequences of Functions
Guy Degla1,2
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Abstract: We stress a basic criterion that shows in a simple way how a sequence of real-valued functions can converge uniformly when it is more or less evident that the sequence converges uniformly away from a finite number of points of the closure of its domain. For functions of a real variable, unlike in most classical textbooks our criterion avoids the search of extrema (by differential calculus) of their general term.
Keywords: Sequence of Functions, Uniform Convergence, Metric, Boundedness
Cite this paper: Degla, G. (2015) A Remark on the Uniform Convergence of Some Sequences of Functions. Advances in Pure Mathematics, 5, 527-533. doi: 10.4236/apm.2015.59048.
References

[1]   Godement, R. (2004) Analysis I. Convergence, Elementary Functions. Springer, Berlin.

[2]   Munkres, J. (2000) Topology. 2nd Edition. Printice Hall, Inc., Upper Saddle River.

[3]   Ross, K.A. (2013) Elementary Analysis. The Theory of Calculus. Springer, New York.
http://dx.doi.org/10.1007/978-1-4614-6271-2

[4]   Godement, R. and Spain, P. (2005) Analysis II: Differential and Integral Calculus, Fourier Series, Holomorphic Fnctions. Springer, Berlin.

[5]   Ezzinbi, K., Degla, G. and Ndambomve, P. (in Press) Controllability for Some Partial Functional Integrodifferential Equations with Nonlocal Conditions in Banach Spaces. Discussiones Mathematicae Differential Inclusions Control and Optimization.

[6]   Freslon, J., Poineau, J., Fredon, D. and Morin, C. (2010) Mathématiques. Exercices Incontournables MP. Dunod, Paris.

 
 
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