Acta Universitatis Lodziensis. Folia Mathematicahttp://hdl.handle.net/11089/41402019-01-18T10:20:08Z2019-01-18T10:20:08ZIdeal Convergence of Sequences and Some of its ApplicationsBalcerzak, MarekFilipczak, Małgorzatahttp://hdl.handle.net/11089/238552018-02-03T02:07:07Z2017-01-01T00:00:00ZIdeal Convergence of Sequences and Some of its Applications
Balcerzak, Marek; Filipczak, Małgorzata
We give a short survey of results on ideal convergence with some
applications. In particular, we present a contribution of mathematicians from Łódź to these investigations during the recent 16 years.
2017-01-01T00:00:00ZSome Non-Measurable SetsKierus, Alicjahttp://hdl.handle.net/11089/181602018-02-01T11:20:30Z2010-01-01T00:00:00ZSome Non-Measurable Sets
Kierus, Alicja
This paper contains constructions of some non-measurable sets,
based on classical Vitali’s and Bernstein’s constructions (see for example [6]).
This constructions probably belong to mathematical folklore, but as far as
we know they are rather hard to be found in literature. It seems that the
constructed sets can be used as examples in some interesting situations.
2010-01-01T00:00:00ZSpatial and age-dependent population dynamics model with an additional structure: can there be a unique solution?Tchuenche, Jean M.http://hdl.handle.net/11089/181592018-02-01T11:20:38Z2013-01-01T00:00:00ZSpatial and age-dependent population dynamics model with an additional structure: can there be a unique solution?
Tchuenche, Jean M.
A simple age-dependent population dynamics model with an additional structure or physiological variable is presented in its variational formulation. Although the model is well-posed, the closed form solution with space variable is difficult to obtain explicitly, we prove the uniqueness of its solutions using the fundamental Green’s formula. The space variable is taken into account in the extended model with the assumption that the coefficient of diffusivity is unity.
2013-01-01T00:00:00ZOn Compact Sets of Compact Operators on Banach Spaces not Containing a Copy of l^1Akkouchi, Mohamedhttp://hdl.handle.net/11089/181572018-02-01T11:20:32Z2010-01-01T00:00:00ZOn Compact Sets of Compact Operators on Banach Spaces not Containing a Copy of l^1
Akkouchi, Mohamed
F. Galaz-Fontes (Proc. AMS., 1998) has established a criterion
for a subset of the space of compact linear operators from a reflexive and
separable space X into a Banach space Y to be compact. F. Mayoral (Proc.
AMS., 2000) has extended this criterion to the case of Banach spaces not
containing a copy of l^1 . The purpose of this note is to give a new proof of the
result of F. Mayoral. In our proof, we use l^∞ -spaces, a well known result of
H. P. Rosenthal and L.E. Dor which characterizes the spaces without a copy
of l^1 and a recent result obtained by G. Nagy in 2007 concerining compact
sets in normed spaces. We point out that another proof of Mayoral’s result
was given by E. Serrano, C. Pineiro and J.M. Delgado (Proc. AMS., 2006) by
using a different method.
2010-01-01T00:00:00Z