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In this paper the authors consider the third order neutral difference equationequation* ^3 (x₍+p₍x₍-₊) +q₍f (x₍-) =h₍equation*where \ p₍\, \ q₍\, \h₍\ \ are real sequences. They use Krasnoselskii's fixed point theorem to establish the existence of nonoscillatory solutions. The results are illustrated with examples. 2000 Mathematics Subject Classification. 39A10
Thandapani et al. (Tue,) studied this question.