Results 21 to 30 of about 2,656 (162)
On further strengthened Hardy‐Hilbert′s inequality
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 27, Page 1423-1427, 2004., 2004 We obtain an inequality for the weight coefficient ω(q, n) (q > 1, 1/q + 1/q = 1, n ∈ ℕ) in the form ω(q,n)=:∑m=1∞(1/(m+n))(n/m)1/q<π/sin(π/p) − 1/(2n1/p + (2/a)n−1/q) where 0 < a < 147/45, as n ≥ 3; 0 < a < (1 − C)/(2C − 1), as n = 1, 2, and C is an Euler constant. We show a generalization and improvement of Hilbert′s inequalities.
Lü Zhongxue
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On Volterra inequalities and their applications
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 3, Page 117-134, 2004., 2004 We present certain variants of two‐dimensional and n‐dimensional Volterra integral inequalities. In particular, generalizations of the Gronwall inequality are obtained. These results are applied in various problems for differential and integral equations.
Lechosław Hącia
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Ostrowski Type Inequalities over Spherical Shells [PDF]
, 2008 2000 Mathematics Subject Classification: 26D10, 26D15.Here are presented Ostrowski type inequalities over spherical shells. These regard sharp or close to sharp estimates to the difference of the average of a multivariate function from its value at a ...
Anastassiou, George A.
core
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this note, we introduce the concept of ℏ‐Godunova–Levin interval‐valued preinvex functions. As a result of these novel notions, we have developed several variants of Hermite–Hadamard and Fejér‐type inequalities under inclusion order relations. Furthermore, we demonstrate through suitable substitutions that this type of convexity unifies a variety of
Zareen A. Khan +4 more
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A lower bound for ratio of power means
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 1, Page 49-53, 2004., 2004 Let n and m be natural numbers. Suppose that {ai} i=1n+m is an increasing, logarithmically convex, and positive sequence. Denote the power mean Pn(r) for any given positive real number r by Pn(r)=((1/n)∑i=1nair) 1/r. Then Pn(r)/Pn+m(r) ≥ an/an+m. The lower bound is the best possible.
Feng Qi, Bai-Ni Guo, Lokenath Debnath
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A Triple Inequality with Series and Improper Integrals [PDF]
, 2006 As a consequence of the Integral Test we find a triple inequality which bounds up and down both a series with respect to its corresponding improper integral, and reciprocally an improper integral with respect to its corresponding series.Comment: 4 ...
Smarandache, Florentin
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A Sharp Simpson’s Second Type Inequality via Riemann–Liouville Fractional Integrals
Journal of Mathematics, Volume 2025, Issue 1, 2025.This paper deals with a new sharp version of Simpson’s second inequality by using the concepts of absolute continuity, Grüss inequality, and Chebyshev functionals. To demonstrate the applicability of the main result, three examples are given. Also, as generalization of the main result, a Simpson’s second type inequality related to the class of Riemann ...
Mohsen Rostamian Delavar +1 more
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Some refinements and generalizations of Carleman′s inequality
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 41, Page 2171-2180, 2004., 2004 We give some refinements and generalizations of Carleman′s inequality with weaker condition for weight coefficient.
Dah-Yan Hwang
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An inequality for means with applications
, 2008 We show that an almost trivial inequality for the first and second mean of a random variable can be used to give non-trivial improvements on deep results. As applications we improve on results on lower bounds for the Riemann zeta-function on the critical
Schlage-Puchta, Jan-Christoph
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Open Mathematics, 2022 In this article, we introduce the notions of generalized fractional integrals for the interval-valued functions (IVFs) of two variables. We establish Hermite-Hadamard (H-H) type inequalities and some related inequalities for co-ordinated convex IVFs by ...
Vivas-Cortez Miguel J. +4 more
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