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Remarks on the Sobolev type spaces of multifunctions

Kasperski A.

Zeszyty Naukowe. Matematyka Stosowana / Politechnika Śląska

2015

z. 5

53--60

In this paper we introduce the spaces of multifunctions SX,pq and Xpq which correspond with the Sobolev space Wpq and the space of multifunctions Xmkc,φ,k,Y which correspond with the Orlicz-Sobolev space Wkφ. We study completeness of them. Also we give some theorems.

W artykule wprowadzamy przestrzenie multifunkcji SXpq and Xpq, które odpowiadają przestrzeni Soboleva Wpq, oraz przestrzeń multifunkcji Xmkc,φ,k,Y , która odpowiada przestrzeni Orlicza-Soboleva Wkφ. Badamy zupełność tych przestrzeni. Podajemy także pewne twierdzenia dotyczące tych przestrzeni.

The "Second Derivative" of a Non-Differentiable Function and its Use in Interval Optimization Methods

Kubica B. J.

Journal of Telecommunications and Information Technology

2011

nr 4

81-85

The paper presents an idea to use weak derivatives in interval global optimization. It allows using the Newton operator to narrow domains of non-differentiable functions. Preliminary computational experiments are also presented.

On II-approximate limits and II-approximate smoothness

Zduńczyk R.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 1

1-16

In this paper we present some results based on slightly modified idea of the I-density introduced by Władysław Wilczyński. Some theorems are generalized versions of results from [2] and [3]. We investigate properties of functions from R^X, where X is supplied with the I-density. We try to free our considerations from the assumption of Baire property, or measurability. In some cases this is not done yet. Star-marked statements still need that assumption, proofs presented here are done for Baire property, but it is possible to adapt them to measure. I-density itself does not require any structure of considered space but a metric vector space over R. However, in last section we confine ourselves to R, for we make use of R’s structure for simplicity. To find more about related topics see [4], [5], more bibliography one can find in [1] and [5].

On a certain criterion of the existence of generalized derivative from Orlicz Class

Borsuk M.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 2

173-178

In terms of difference quotients it is established the existence of generalized derivative of the function.