HYPERBOLIC SINE FUNCTION IN HILBERTíS DISCRETE INEQUALITY OF THREE VARIABLES
Abstract views: 12 / PDF downloads: 12
Keywords:
Hilbert’s inequality of discrete form, Hölder inequality, Best constant, Hyperbolic Sine FunctionAbstract
Through this manuscript, we deduce a new discrete form of Hilbertís inequality of three variables of Hyperbolic Sine Function, also, we will show that the constant in
the main inequality is the best constant. Also, we will give the reverse form of the main
inequality and the equivalent forms of it
References
A. Kufner, L. Maligranda, L.E. Persson, The Hardy inequality: About its history and some related results, Vydavatelsk
servis, Pilsen, 2007.
A. Kufner, L. Maligranda, L.E. Persson, The prehistory of the Hardy inequality, Amer. Math. Monthly, 113 (2006)
–732.
Al-Oushoush Kh.Nizar, L.E. Azar, Ahmad H.A. Bataineh, A Sharper Form of Half-Discrete Hilbert Inequality Related
to Hardy Inequality, Filomat, 32(19) (2018), 6733–6740.
B. Yang, The norm of operator and Hilbert-Type Inequalities, scince press, Beijing, China (2009).
B. Yang, T. M. Rassias, On the way of weight coefficients and research for the Hilbert-type inequalities, Math. Inequal.
Appl. 6 (2003), 625–658.
G. H. Hardy, J.E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press, London, (1952).
L.E.Azar, Tow new forms of Hilbert integral inequality, Math. Inequal. Appl. 17 (2014).
M. Krnic, G. Mingzhe, J. Pecaric, G. Xuemei, On the best constant in Hilbert’s inequality, Math.Inequal.Appl. 8(2)
(2005), 317–329.
M. Krnic, J. Pecaric, Extension of Hilbert’s inequality, J. Math. Anal. Appl. 324 (2006), 150–160.
M. Krnic, J. Pecaric, General Hilbert’s and Hardy’s inequalities, Math. Inequal. Appl. 8 (2005), 29–52.
M. Krnic, A refined discrete Hilbert inequality via the Hermite-Hadamard inequality, Comput. Math. Appl. 63 (2012),
–1596.
Nizar Kh. Al-Oushoush, New Discrete Hilbert Inequality For Three Variables, JMA, 13(3) (2022), pp 56–67.
Ricai Luo, and Bicheng Yang, Parameterized discrete Hilbert-type inequalities with intermediate variable, Journal of
Inequalities and Applications, 142 (2019).
Ts. Batbold, L.E.Azar, A new form of Hilbert Integral inequaltity, JMI, 12(2) (2018), 379–390.
Ts. Batbold, L.E.Azar, Discrete analogues of Hilbert integral inequalities for three variables, Journal of Inequalities
and Special function, 9 (2018), 66–76.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Results in Nonlinear Analysis
This work is licensed under a Creative Commons Attribution 4.0 International License.