Results 31 to 40 of about 1,205 (159)
A monotonicity property involving the generalized elliptic integral of the first kind
, 2017 In this paper, we prove that the function r → Y (r) = Ka(r) sin(πa)r′2 log(eR(a)/2/r′) − 1 r′2 is strictly increasing from (0,1) onto (π/[R(a)sin(πa)]−1,a(1−a)) for all a∈ (0,1/2] , where r′ = √ 1− r2 , Ka(r) is the generalized elliptic integral of the ...
Zhen-Hang Yang, Y. Chu
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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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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
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Refinements of quantum Hermite-Hadamard-type inequalities
Open Mathematics, 2021 In this paper, we first obtain two new quantum Hermite-Hadamard-type inequalities for newly defined quantum integral. Then we establish several refinements of quantum Hermite-Hadamard inequalities.
Budak Hüseyin +3 more
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, 2018 By using real analysis technique and the method of weight functions, the necessary and sufficient conditions for the validity of Hilbert type integral inequalities with a class of quasi-homogeneous kernels and the best constant factors are obtained, and ...
Yong Hong, B. He, Bicheng Yang
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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
On a new generalization of some Hilbert-type inequalities
Open Mathematics, 2021 In this work, by introducing several parameters, a new kernel function including both the homogeneous and non-homogeneous cases is constructed, and a Hilbert-type inequality related to the newly constructed kernel function is established.
You Minghui, Song Wei, Wang Xiaoyu
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Ostrowski type fractional integral inequalities for MT-convex functions
, 2015 Some inequalities of Ostrowski type for MT-convex functions via fractional integrals are obtained. These results not only generalize those of [25], but also provide new estimates on these types of Ostrowski inequalities for fractional integrals.
Wenjun Liu
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On Improved Simpson‐Type Inequalities via Convexity and Generalized Fractional Operators
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this work, we develop novel Simpson‐type inequalities for mappings with convex properties by employing operators for tempered fractional integrals. These findings expand upon and refine classical results, including those linked to Riemann–Liouville fractional integrals.
Areej A. Almoneef +4 more
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Open Mathematics, 2021 In this study, we first obtain a new identity for generalized fractional integrals which contains some parameters. Then by this equality, we establish some new parameterized inequalities for co-ordinated convex functions involving generalized fractional ...
Kalsoom Humaira +3 more
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