A Remark on the Uniform Convergence of Some Sequences of Functions
Author(s)
Guy Degla1,2
Affiliation(s)
1 Institut de Mathematiques et de Sciences Physiques (IMSP), Porto-Novo, Benin. 2 International Centre for Theoretical Physics (ICTP), Trieste, Italy.
1 Institut de Mathematiques et de Sciences Physiques (IMSP), Porto-Novo, Benin. 2 International Centre for Theoretical Physics (ICTP), Trieste, Italy.
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.
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.
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.
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.
[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.