Some New Volterra-Fredholm-Type Discrete Inequalities and Their Applications in the Theory of Difference Equations
نویسندگان
چکیده
and Applied Analysis 3 Remark 2.4. Lemma 2.3 is a direct variation of 19, Lemma 2.5 β1 , and we note a m,n ≥ 0 here. Theorem 2.5. Suppose that u m,n , a m,n ∈ ℘ Ω , bi s, t,m, n , ci s, t,m, n ∈ ℘ Ω2 , i 1, 2, . . . , l1, di s, t,m, n , ei s, t,m, n ∈ ℘ Ω2 , i 1, 2, . . . , l2 with bi, ci, di, ei nondecreasing in the last two variables. p, qi, ri are nonnegative constants with p ≥ qi, p ≥ ri, i 1, 2, . . . , l1, p / 0, while hi, ji are nonnegative constants with p ≥ hi, p ≥ ji, i 1, 2, . . . , l2. If, for m,n ∈ Ω, u m,n satisfies
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