Abstract
In this paper, we give some Minkowski–Clarkson’s type inequalities related to
two finite sequences of real nonnegative numbers. In particular, we prove
two inequalities which in some sense can be regarded as inverse Minkowski’s
inequalities concerning the cases
References
[1] F. Alrimawi, O. Hirzallah and F. Kittaneh, Norm inequalities related to Clarkson inequalities, Electron. J. Linear Algebra 34 (2018), 163–169. 10.13001/1081-3810.3642Search in Google Scholar
[2] H. Alzer and S. Ruscheweyh, A converse of Minkowski’s inequality, Discrete Math. 216 (2000), no. 1–3, 253–256. 10.1016/S0012-365X(99)00350-7Search in Google Scholar
[3] E. F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin, 1961. 10.1007/978-3-642-64971-4Search in Google Scholar
[4] J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396–414. 10.1090/S0002-9947-1936-1501880-4Search in Google Scholar
[5] D. E. Daykin and C. J. Eliezer, Generalization of Hölder’s and Minkowski’s inequalities, Proc. Cambridge Philos. Soc. 64 (1968), 1023–1027. 10.1017/S0305004100043747Search in Google Scholar
[6] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge University, Cambridge, 1952. Search in Google Scholar
[7] R. Meštrović, Minkowski–Clarkson’s like inequalities, New Zealand J. Math. 44 (2014), 107–111. Search in Google Scholar
[8] R. Meštrović and D. Kalaj, A converse of Minkowski’s type inequalities, J. Inequal. Appl. 2010 (2010), Article ID 461215. 10.1155/2010/461215Search in Google Scholar
[9] D. S. Mitrinović, Analytic Inequalities, Springer, New York, 1970. 10.1007/978-3-642-99970-3Search in Google Scholar
[10] D. S. Mitrinović, J. E. Pečarić and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic, Dordrecht, 1993. 10.1007/978-94-017-1043-5Search in Google Scholar
[11] H. Tôyama, On the inequality of Ingham and Jessen, Proc. Japan Acad. 24 (1948), 10–12. 10.3792/pja/1195572073Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
