Some Bessel type additive inequalities in inner product spaces
DOI:
https://doi.org/10.24193/subbmath.2021.2.13Keywords:
Inner product spaces, Bessel’s inequality, Schwarz’s inequality.Abstract
In this paper we obtain some additive inequalities related to the cele- brated Bessel’s inequality in inner product spaces. They complement the results obtained by Boas-Bellman, Bombieri, Selberg and Heilbronn, which have been applied for almost orthogonal series and in Number Theory.
Mathematics Subject Classification (2010): 46C05, 26D15.
References
Bellman, R., Almost orthogonal series, Bull. Amer. Math. Soc., 50(1944), 517-519.
Boas, R.P., A general moment problem, Amer. J. Math., 63(1941), 361-370.
Bombieri, E., A note on the large sieve, Acta Arith., 18(1971), 401-404.
Dragomir, S.S., Discrete Inequalities of the Cauchy-Buniakowsky-Schwartz Type, Nova Science Publishers, Inc., Hauppauge, NY, 2004, x+225 pp., ISBN: 1-59454-049-7.
Dragomir, S.S., Advances in Inequalities of the Schwarz, Gru¨ss and Bessel Type in Inner Product Spaces, Nova Science Publishers, Inc., Hauppauge, NY, 2005, viii+249 pp., ISBN: 1-59454-202-3.
Dragomir, S.S., Advances in Inequalities of the Schwarz, Triangle and Heisenberg Type in Inner Product Spaces, Nova Science Publishers, Inc., New York, 2007, xii+243 pp., ISBN: 978-1-59454-903-8; 1-59454-903-6.
Dragomir, S.S., On the Boas-Bellman inequality in inner product spaces, Bull. Austral. Math. Soc., 69(2004), no. 2, 217-225. Preprint RGMIA Res. Rep. Coll., 6(2003), Supplement, Article 14.
Dragomir, S.S., On the Bombieri inequality in inner product spaces, Libertas Math., 25(2005), 13-26. Preprint RGMIA Res. Rep. Coll., 6(2003), No. 3, Article 5.
Dragomir, S.S., Some Bombieri type inequalities in inner product spaces, J. Indones. Math. Soc., 10(2004), no. 2, 91-98. Preprint RGMIA Res. Rep. Coll., 6(2003), Supplement, Article 16.
Dragomir, S.S., Mond, B., On the Boas-Bellman generalisation of Bessel’s inequality in inner product spaces, Italian J. of Pure & Appl. Math., 3(1998), 29-35.
Dragomir, S.S., Mond, B., Pecaric, J.E., Some remarks on Bessel’s inequality in inner product spaces, Stud. Univ. Babes-Bolyai Math., 37(1992), no. 4, 77-86.
Dragomir, S.S., Sandor, J., On Bessels’s and Gram’s inequalities in prehilbertian spaces, Periodica Math. Hungarica, 29(1994), no. 3, 197-205.
Heilbronn, H., On the averages of some arithmetical functions of two variables, Mathematica, 5(1958), 1-7.
Mitrinovic, D.S., Pecaric, J.E., Fink, A.M., Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht/Boston/London, 1993.
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