References
- A. Z. Alimagambetova and R. Oinarov, Criteria for the oscillation and nonoscillation of a second-order semilinear difference equation, Mat. Zh. 7 (2007), no. 1(23), 15-24.
- G. Bennett, Some elementary inequalities, Quart. J. Math. Oxford Ser. (2) 38 (1987), no. 152, 401-425. https://doi.org/10.1093/qmath/38.4.401
- G. Bennett, Some elementary inequalities. II, Quart. J. Math. Oxford Ser. (2) 39 (1988), no. 156, 385-400. https://doi.org/10.1093/qmath/39.4.385
- P. Gao, Hardy-type inequalities via auxiliary sequences, J. Math. Anal. Appl. 343 (2008), no. 1, 48-57. https://doi.org/10.1016/j.jmaa.2008.01.024
-
P. Gao, On
$l^p$ norms of weighted mean matrices, Math. Z. 264 (2010), no. 4, 829-848. https://doi.org/10.1007/s00209-009-0490-2 - G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press, Cambridge, 1988.
- P. Hasil and M. Vesely, Critical oscillation constant for difference equations with almost periodic coeffcients, Abstr. Appl. Anal. 2012 (2012), Art. ID 471435, 19 pp. https://doi.org/10.1155/2012/471435
- P. Hasil and M. Vesely, Oscillation and non-oscillation criteria for linear and half-linear difference equations, J. Math. Anal. Appl. 452 (2017), no. 1, 401-428. https://doi.org/10.1016/j.jmaa.2017.03.012
- A. Kalybay, D. Karatayeva, R. Oinarov, and A. Temirkhanove, Oscillation of a second order half-linear difference equation and the discrete Hardy inequality, Electron. J. Qual. Theory Differ. Equ. 2017 (2017), Paper No. 43, 16 pp. https://doi.org/10.14232/ejqtde.2017.1.43
- A. Kufner, L. Maligranda, and L.-E. Persson, The Hardy inequality, Vydavatelsky Servis, Plzen, 2007.
- A. Kufner and L.-E. Persson, Weighted inequalities of Hardy type, World Scientific Publishing Co., Inc., River Edge, NJ, 2003. https://doi.org/10.1142/5129
- L. Maligranda, R. Oinarov, and L.-E. Persson, On Hardy q-inequalities, Czechoslovak Math. J. 64(139) (2014), no. 3, 659-682. https://doi.org/10.1007/s10587-014-0125-6
- B. Muckenhoupt, Hardy's inequality with weights, Studia Math. 44 (1972), 31-38. https://doi.org/10.4064/sm-44-1-31-38
- R. Oinarov, Oscillation of second order half-linear differential equation and weighted Hardy inequality, Mat. Zh. 12 (2012), no. 3, 149-155.
- B. Opic and A. Kufner, Hardy-type inequalities, Pitman Research Notes in Mathematics Series, 219, Longman Scientific & Technical, Harlow, 1990.
- L.-E. Persson, R. Oinarov, and S. Shaimardan, Hardy-type inequalities in fractional h-discrete calculus, J. Inequal. Appl. 2018 (2018), Paper No. 73, 14 pp. https://doi. org/10.1186/s13660-018-1662-6
- P. Rehak, Oscillatory properties of second order half-linear difference equations, Czechoslovak Math. J. 51(126) (2001), no. 2, 303-321. https://doi.org/10.1023/A:1013790713905
- M. Vesely and P. Hasil, Oscillation and nonoscillation of asymptotically almost periodic half-linear difference equations, Abstr. Appl. Anal. 2013 (2013), Art. ID 432936, 12 pp. https://doi.org/10.1155/2013/432936