The main result of the paper (Theorem 3) concerns a linear discrete inequality of the type
all the functions x, p, are real-valued and nonnegative, p - nondecreasing, in n for every fixed. In the first two theorems some special cases of (*) are considered. Theorems 3, 4 concern nonlinear inequalities with H nonnegative, strictly increasing, subadditive, , and furthermore (Theorem 3); H - submultiplicative, g - nonnegative (Theorem 4). Linear inequalities are discrete analogies of those proved by the author in J. Math. Anal. Appl. 103, 184-197 (1984; Zbl 0573.26008) and extend many results proved by B. G. Pachpatte [e.g. Indian J. Pure Appl. Math. 8, 1093-1107 (1977; Zbl 0402.26008)]. See also R. P. Agarwal and E. Thandapani [Bull. Inst. Math., Acad. Sin. 9, 235-248 (1981; Zbl 0474.26009); An. Ştiinţ. Univ. Al. I. Cuza Iaşi, N. Ser., Secţ. Ia 28, 71-75 (1982; Zbl 0553.26004)].