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A new generalization of the $l_p$ spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 15، دوره 16، شماره 5، مرداد 2025، صفحه 165-172 اصل مقاله (346.97 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.27002.3472 | ||
| نویسنده | ||
| Alireza Moazzen* | ||
| Department of Mathematics, Kosar University of Bojnord, Bojnord, Iran | ||
| تاریخ دریافت: 02 خرداد 1401، تاریخ پذیرش: 27 خرداد 1402 | ||
| چکیده | ||
| In this work, using semidefinite matrices gives a new generalization of the $l_p$ spaces and some inequalities containing lower bounds of some operators are proved. Also, by defining an inner product on the classes of an equivalence relation on operators, some inequalities similar to the well-known inequalities including the Copson, Cesaro, Hilbert and Hardy inequalities are obtained. | ||
| کلیدواژهها | ||
| Lower bound of operator؛ Hilbert's operator؛ Cesaro operator | ||
| مراجع | ||
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[1] E.F. Beckenbach and R. Bellman, Inequalities, Springer, Berlin, 1961. [2] G. Bennett, Factorizing the classical inequalities, Mem. Amer. Math. Soc. 576 (1996). [3] G. Bennett, Lower bounds for matrices, Linear Algebra Appl. 82 (1986), 81–98. [4] F.T. Copson, Note on series of positive terms, J. Lond. Soc. 1 (1928), no. 1, 49–51. [5] G.J.O. Jameson and R. Lashkaripour, Norms of certain operators on weighted lp spaces and Lorentz sequence spaces, J. Inequal. Pure Appl. Math. 3 (2002), no. 1, Article 6. [6] G.J.O. Jameson, Norms and lower bounds of operators on the Lorentz sequence spaces d(w, 1), Illinois J. Math. 43 (1999), 79–99. [7] R. Lyons, A lower bound for the Ceasaro operator, Proc. Amer. Math. Soc. 86 (1982), 694. [8] P.C. Mahalanobis, On the generalised distance in statistics, Proc. Nat. Inst. Sci. India 2 (1936), no. 1, 49–55. | ||
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