In this paper, some reverse Hilbert-Pachpatte's type inequalities involving series of nonnegative terms are established, which provide new estimates on inequality of this type.

In this paper, vector norm inequalities that provides upper bounds for the Lipschitz quantitybounded linear operators T, V on the Hilbert space H and vectors x ∈ H are established. Applications in relation to HermiteHadamard type inequalities and examples for elementary functions of interest are given as well.

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