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A viability result for Carathéodory non-convex differential inclusion in Banach spaces

Charradi Nabil, Sajid Saïd

Opuscula Mathematica

2023

Vol. 43, no. 5

621--632

This paper deals with the existence of solutions to the following differential inclusion: x˙ (t) ∈ F(t, x(t)) a.e. on [0, T[ and x(t) ∈ K, for all t ∈ [0, T], where F : [0, T] × K → 2E is a Carathéodory multifunction and K is a closed subset of a separable Banach space E.

On the fractional Pettis and Aumann-Pettis integral for multifunctions

Ibrahim A-G., Soliman A.M.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 2

181-200

Let L be a positive real number. In the present paper we present the definition of the Aumann Pettis integral and the Pettis integral of order for multifunctions. The properties of these integrals and the relations between them are studied extensively. In particular, a Strassen type theorem in this case and continuation property are proved. Also, we give a version for Fatou’s lemma and dominated convergence theorem for the Aumann-Pettis integral of order and for multifunctions.

Frechet type theorem and its applications to multifunctions

Kubiś B., Kubiś W.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 2

165-170

We state a Frechet type theorem for measurable maps with values in an almost arcwise connected metrizable space. As an application, we obtain some results on continuous approximation of measurable multifunctions.