Some inequalities of Aczel type for Gramians in n-inner product spaces

• Autorzy: Rafiq A. , Mir N. , Hussain S.
• Języki publikacji: PL

Abstrakty

EN

Some inequalities of Aczel type for Gramians in n-inner product spaces which generalize pecaric result for n-inner product spaces are given. Applications connected to Schwartz’s inequality for n-inner product spaces are also noted.

Słowa kluczowe

PL

nierówności Aczela; nierówności Kurepa; nierówności Schwartza; przestrzeń unitarna

EN

Aczel inequalities; Kurepa inequalities; Schwartz inequalities; unitary spaces

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2007
• Tom: Vol. 40, nr 3
• Strony: 609--629
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Rafiq A.

autor

Mir N.

autor

Hussain S.

• Department of Mathematics Comsats Institute of Information Technology Islamabad, Pakistan,

Bibliografia

• [1] Y. J. Cho, M. Matić and J. Pečarić, On Grams determinant in n-inner product Spaces, Bull. Korean Math. Soc. 41 (4) (2004), 739-777.
• [2] Y. J. Cho, On Gram's determinant in 2-inner product spaces, J. Korean Math. Soc. 38 (6) (2001), 1156-1125.
• [3] Y. J. Cho, P. C. S. Lin, S. S. Kim and A. Misiak, Theory of 2-inner product spaces, Nova Science Publishers, Inc. 1999.
• [4] S. S. Dragomir, A refinement of Cauchy-Schwartz's inequality, Gaz. Mat. Metod. (Bucharest) 8 (1987), 94-95, ZBL 632:26010.
• [5] S. S. Dragomir, Some refinements of Cauchy-Schwartz's inequality, ibid. 10 (1989), 93-95.
• [6] S. S. Dragomir and J. Sandor, Some inequalities in prehilbertian spaces, Studia Univ., Babes-Bolyai, Mathematica 32 (1) (1987), 71-78 MR 89h: 46034.
• [7] S. S. Dragomir and N. M. Ionescu, A refinement of Gram's inequality in inner product spaces, Proc. 4th Symp. Math. Appli., Nov. 1991, Timisoara, 188-191.
• [8] S. S. Dragomir, On Aczel's inequality in inner product spaces, Acta Math. Hungarica 65 (2) (1994), 141-148.
• [9] S. S. Dragomir and B. Mond, Some inequalities of Aczel type for Gramians in inner product spaces, RGMIA Res. Rep. Coll. 2 (2), Article 10, 1999.
• [10] S. S. Dragomir and J. Sandor, On Bessel's, Gram's inequalities in prehilbertian spaces, Periodica Math. Hungarica, Math. Hung. 29 (3) (1994), 197-205.
• [11] S. Kurepa, On the Buniakowsky-Cauchy-Schwarz's inequality, Glasnik Mat. Ser. III 1 (21) (1966), 147-158.
• [12] S. Kurepa, Note on inequalities associated with Hermitian functionals, Glasnik Mat. Ser. III 3 (23) (1968), 197-206.
• [13] D. S. Mitrinovic, J. E. Pecarič and A. M. Fink, Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht/Boston/London, 1993.
• [14] J. E. Pecarič, On some classical inequalities in unitary spaces, Mat. Bilten (Skopje) 16 (1992), 63-72.