Results 21 to 30 of about 1,866 (138)
Refined and Generalized Versions of Hölder’s Inequality via Schur Convexity of Functions
Journal of Function Spaces, Volume 2025, Issue 1, 2025.In this paper, we introduce a class of functions associated with Hölder’s inequality and show the Schur convexities of these functions. With the help of Schur convexity, several improved versions of Hölder’s inequality are established. The results obtained here are the generalizations and refinements of the existing results for Hölder’s inequality.
Shanhe Wu, Raúl E. Curto
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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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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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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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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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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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Pre-Schur convex functions and some integral inequalities on domains from plane
Acta Universitatis Sapientiae: Mathematica, 2023 In this paper we introduce the concept of pre-Schur convex functions defined on general domains from plane. Then, by making use of Green’s identity for double integrals, we establish some integral inequalities for this class of functions that naturally ...
Dragomir Silvestru Sever
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Some Hermite–Hadamard Type Inequality for the Operator p,P‐Preinvex Function
Journal of Mathematics, Volume 2025, Issue 1, 2025.The goal of the article is to introduce the operator p,P‐preinvex function and present several features of this function. Also, we establish some Hermite–Hadamard type inequalities for this function.
Mahsa Latifi Moghadam +3 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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