Results 21 to 30 of about 2,031 (186)
Three weights higher order Hardy type inequalities
Journal of Function Spaces, Volume 4, Issue 2, Page 163-191, 2006., 2006 We investigate the following three weights higher order Hardy type inequality (0.1) ‖g‖q,u≤C‖Dρkg‖p,v where Dρi denotes the following weighted differential operator: dig(t)dti,i=01…1,,,m-,di-mdti-m(p(t)dmg(t)dtm),i=m,m+1…,,k, for a weight function ρ(·). A complete description of the weights u, v and ρ so that (0.1) holds was given in [4] for the case 1
Aigerim A. Kalybay +2 more
wiley +1 more source
A Mulholland-type inequality in the whole plane with multi parameters
Journal of King Saud University: Science, 2020 By introducing independent parameters, and applying the weight coefficients, we give a new Mulholland-type inequality in the whole plane with a best possible constant factor.
Bing He, Bicheng Yang
doaj
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
wiley +1 more source
On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals
, 2017 In this paper, we have established Hermite-Hadamard-type inequalities for fractional integrals and will be given an identity. With the help of this fractional-type integral identity, we give some integral inequalities connected with the left-side of ...
M. Sarıkaya, H. Yildirim
semanticscholar +1 more source
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
wiley +1 more source
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 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
wiley +1 more source
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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Refinement of the Jensen integral inequality
Open Mathematics, 2016 In this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.
Sever Dragomir Silvestru +2 more
doaj +1 more source