The area of solutions of linear difference Hukuhara equations

I. V. Atamas’

Abstract


In this paper we study the question of area calculation for solutions to linear difference Hukuhara equations H n n X AX  . We introduce here auxiliary sequences , , k k n n n  S X A X k        . Then we can write a comparison system in abstract form       n n  1 with initial conditions   0 2 n n      , where operator :l l    is given by   1 1, 1 k k k    k       ,  0 1    2 . Examining a comparison system, we get a main result: we obtain the exact formula for area S X X  n n ,  for solutions to linear difference Hukuhara equations:             2 2 2 0 0 0 0 0 1 0 1 ! 1 , 2 ! , 2 , .

Keywords


Hukuhara difference; Minkowski mixed area; Chaplygin-Vazhevskii method of comparison; difference equations; dynamic systems; Hausdorff metric

References


Lakshmikantham V.(2006). Theory of set differential equations in metric spaces.

Cambridge Scientific Publisers, 212 p.

Bhaskar G.(2004). Stability results for Set Difference Equations. Dynamical Systems

and Applications, р. 479-485.

Daletskii Yu.L., Krein M.G. (1970). Stability of Solutions of Differential Equations

in Banach Space. Translations of Mathematical Monographs Reprinted by AMS, 536 р.

Slyn'ko V.I. (2016). The stability of fixed points of discrete dynamical systems in the

space

n

conv . Functional Analysis and Applications, 163–165.

Slyn'ko V.I. ( 2017). Stability in terms of two measures for set difference equations in

space

n

conv . Applicable Analysis, p. 278–292.

Blyashke W. (1967). Kreis und Kugel.Verlag von Veit & Comp., 232 p.

Slyn'ko V.I. (2016). The area of solutions for a class of set linear differential

equations with Hukuhara derivative. Math. notes (to appear).


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