Origin and evolution of South Arabian minuscule writing on by J. Ryckmans

By J. Ryckmans

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27 it follows that F D F1 F2 is upper semicontinuous. 31. Let each of the mappings F W X ! Y /, G W X ! Y / be upper semicontinuous and lower semicontinuous and the space Y be Hausdorff. y/g is closed in X . Let us consider one class of the multivalued mappings operating in Banach spaces. Let X1 , X2 , X3 are Banach spaces and X D X1 X2 X3 . i D 1; 2; 3/ be the space of linear functionals that divide points in Xi . 1 The Main Results from Multivalued Mapping Theory 17 continuous. The sequence fyn g Xi is -weakly converges to the element y in Xi (yn !

Obviously, the definitional domain D. / of the operator is not dense in X , therefore the dual W D. / X ! ˝// . ˝// and all previous Propositions are valid for it. Let us consider a dynamic system, generated by an evolutionary inclusion with vector (affine) processes. A/ X ! X /. 8) is valid for all t 2 Œ0; T . 9) form the m-semiflow, consisting of vector processes. 8)g. A/ ! A// is the m-semiflow. t; / is a vector process. 8) with initial conditions x01 and x02 respectively. 8) with the initial condition x01 C x02 .

Y Z/ is also upper semicontinuous. In applications, starting from the given multivalued mappings F1 W E ! 2X , F2 W E ! 2Y we can construct the mapping F W E ! , F1 D FX , F2 D FY . X / D . x/ is called a diagonal product of the mappings F1 and F2 and denoted by F D F1 4F2 . From the definition of the mapping F it follows that the diagram F1 2X - ˘X E #F 2X F2 ! , F1 D ˘X ı F , F2 D ˘Y ı F . 8. 27 are valid. Let F1 W X1 ! 2Y1 , F2 W X2 ! x2 / ˚ D . x1 /; X2 ! x2 / is called a Cartesian product of F1 and F2 and it is denoted by F D F1 F2 .

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