A linear Volterra difference equation of non-convolution type of the formKðn; iÞxðiÞ;Sufficient conditions for the existence of a bounded solution of this equation are given. Using this result, an asymptotic equivalence of some solution and given sequence, depending on terms of sequence b, is presented. Finally, the existence of a solution of the considered Volterra equation estimated by a given sequence is obtained.

In this paper we study sphere coverage issue. A sphere of radius one in a 3-dimensional Euclidean space is given. We consider random location of N spherical caps on a sphere, assuming that N is a discrete stochastic variable with a Poisson distribution. Using suitable difference equation, the expected area of the covered region is investigated.

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