Paper's Title:

The ε-Small Ball Drop Property

Author(s):

C. Donnini and A. Martellotti

Dipartimento di Statistica e Matematica per la Ricerca Economica,
Università degli Studi di Napoli "Parthenope",
Via Medina, 80133 Napoli,
Italy
chiara.donnini@uniarthenope.it

{Dipartimento di Matematica e Informatica,
Università degli Studi di Perugia,
Via Pascoli - 06123 Perugia,
Italy.
amart@dipmat.unipg.it
URL: www.dipmat.unipg.it/~amart/

Abstract:

We continue the investigation on classes of small sets in a Banach space that give alternative formulations of the Drop Property. The small sets here considered are the set having the small ball property, and we show that for sets having non-empty intrinsic core and whose affine hull contains a closed affine space of infinite dimension the Drop Property can be equivalently formulated in terms of the small ball property.

Paper's Title:

Existence Results for Second Order Impulsive Functional Differential Equations with Infinite Delay

Author(s):

M. Lakrib, A. Oumansour and K. Yadi  

Laboratoire de Mathématiques, Université Djillali
Liabées, B.P. 89 Sidi Bel Abbès 22000, Algérie
mlakrib@univ-sba.dz
oumansour@univ-sba.dz

Laboratoire de Mathématiques, Université Abou Bekr
Belkaid, B.P. 119 Tlemcen 13000, Algérie
k_yadi@mail.univ-tlemcen.dz

Abstract:

In this paper we study the existence of solutions for second order impulsive functional differential equations with infinite delay. To obtain our results, we apply fixed point methods.

Paper's Title:

The boundedness of Bessel-Riesz operators on generalized Morrey spaces

Author(s):

Mochammad Idris, Hendra Gunawan and Eridani

Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
E-mail: mochidris@students.itb.ac.id

Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
E-mail: hgunawan@math.itb.ac.id
URL: http://personal.fmipa.itb.ac.id/hgunawan/

Department of Mathematics,
Airlangga University,
Surabaya 60115,
Indonesia.
E-mail: eridani.dinadewi@gmail.com

Abstract:

In this paper, we prove the boundedness of Bessel-Riesz operators on generalized Morrey spaces. The proof uses the usual dyadic decomposition, a Hedberg-type inequality for the operators, and the boundedness of Hardy-Littlewood maximal operator. Our results reveal that the norm of the operators is dominated by the norm of the kernels.

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