Extension of linear functionals on pseudonormed linear spaces

on the effect of linear & non-linear texts on students comprehension and recalling

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Minimizing Functionals on Normed - linear Spaces

This paper extends results of [1], [2], of Goldstein, and [3] of Vainberg concerning steepest descent and related topics. An example Is given taken from a simple rendezvous problem in control theory. The problem is one of minimizing a norm on an affine subspace. The problem here is solved in the primal. A solution in the dual is given by Neustadt [4]. I. GENERATION OF MINIMIZING SEQUENCES Let E...

Linear Functionals on Certain Banach Spaces

ON APPROXIMATION OF LINEAR FUNCTIONALS ON Lp SPACES

In a recent paper certain approximations to continuous nonlinear functionals de-ned on an L p space (1 < p < 1) are shown to exist. These approximations may be realized by sigmoidal neural networks employing a linear input layer that implements nite sums of integrals of a certain type. In another recent paper similar approximation results are obtained using elements of a general class of contin...

Linear Functionals and Integrals in Abstract Spaces

In his addendum to Saks, Theory of the Integral, Banach considers a Lebesgue integral defined in a manner quite similar to that of Daniell and remarks that no use is made of a measure. I t is, however, quite easy to show that Banach's and Daniell's integrals are expressible as Lebesgue integrals whose measure functions are regular outer measures in the sense of Carathéodory. In the first two se...