Some problems about the limit of a real-valued function
Kragujevac Journal of Mathematics, Tome 24 (2002), p. 71
Cet article a éte moissonné depuis 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
@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/}
}
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/