Some problems about the limit of a real-valued function
Kragujevac Journal of Mathematics, Tome 24 (2002), p. 71
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
Kragujevac J. Math. 24 (2002) 71-79.
SOME PROBLEMS ABOUT THE LIMIT
OF A REAL-VALUED FUNCTIONDimitrije HajdukovicMilana Babica 5, 51000 Banja Luka, BiH
(Received June 20, 2001)
1. In [1] S. Banach solved the problem of the existence
of a (non-unique) linear shift-invariant functional on the space
of all bounded functions defined on the semi-axis t � 0.
2. Let now a be sufficiently large (written a > a0 for
some a0). Denote by W the real vector space of all
real-valued functions on [0,�) and bounded on [a,�).
This paper is organized as follows. First we will show the
existence of a family of functionals on the space W
containing Banach shift-invariant functionals. Next, by these
functionals we shall define the limit of f(t) as t��,
f � W, and show that this definition is equivalent to the
classical definition of this limit. Further, we show some theorems
characterizing the limit of a function f(t), t � 0 as
t�+�. Each of these theorems gives an answer to the
question what (new) conditions must satisfy a function f � W such that the limit of f(t) as t�+� exists.
Keywords:
limit, real-valued functions
Dimitrije Hajduković. Some problems about the limit of a real-valued function. Kragujevac Journal of Mathematics, Tome 24 (2002), p. 71 . http://geodesic.mathdoc.fr/item/KJM_2002_24_a7/
@article{KJM_2002_24_a7,
author = {Dimitrije Hajdukovi\'c},
title = {Some problems about the limit of a real-valued function},
journal = {Kragujevac Journal of Mathematics},
pages = {71 },
year = {2002},
volume = {24},
language = {en},
url = {http://geodesic.mathdoc.fr/item/KJM_2002_24_a7/}
}