Reverse Hilbert type inequalities

Abstract

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.

A Study on Some New Reverse Hilbert‐Type Inequalities and Its Generalizations on Time Scales

“…In Section 2, we cover some fundamentals of time scale theory as well as several time scale lemmas that will be useful in Section 3, where we prove our findings. As specific examples (when T � N), our major results yield (4), (8), and (10) proven by Zhao and Cheung [3].…”

“…Remark 3. As a special case of eorem 3, if T � N, f(η) � g(η) � 1 and β � ] � 2, we can get (10) proved by Zhao and Cheung [3].…”

“…where (1/d) + (1/l) 1, λ 2 − ((1/d) + (1/l)) 1, and the constant factor K(d, l) is sharp. In [3], the authors showed that if 0 ≤ d, l ≤…”

“…⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ If T � N, f(η) � g(η) � 1 and β � ] � 2,in eorem 1, then we obtain (4) demonstrated in[3]. Let z ∈ T and λ, ω be nonnegative functions.Also, we assume that d, l, f, g are positive functions.…”

On an Extension of a Hardy–Hilbert-Type Inequality with Multi-Parameters

“…Inequalities ( 1) and ( 2) are important in analysis and its applications (cf. [1][2][3][4][5][6][7][8][9][10][11][12]).…”