Approximations of the images and integral funnels of the $L_p$ balls under a Urysohn-type integral operator.
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25.12.2022Üst veri
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Huseyin, A., Huseyin, N. & Guseinov, K.G. Approximations of the Images and Integral Funnels of the Lp Balls under a Urysohn-Type Integral Operator. Funct Anal Its Appl 56, 269–281 (2022).Özet
Approximations of the image and integral funnel of a closed ball of the
space $L_p$, $p>1$, under a Urysohn-type integral operator are considered. A closed ball of the space $L_p$, $p>1$, is replaced by a set consisting of a finite number of piecewise constant functions, and it is proved that, for appropriate discretization parameters, the images of these piecewise constant functions form an internal approximation of the image of the closed ball. This result is applied to approximate the integral funnel of a closed ball of the space $L_p$, $p>1$, under a Urysohn-type integral operator by a set
consisting of a finite number of points.