Improved estimates for the triangle inequality (original) (raw)
Abstract
We obtain refined estimates of the triangle inequality in a normed space using integrals and the Tapia semi-product. The particular case of an inner product space is discussed in more detail.
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References (21)
- Diaz, JB, Metcalf, FT: A complementary triangle inequality in Hilbert and Banach spaces. Proc. Am. Math. Soc. 17, 88-97 (1966)
- Dragomir, SS: Reverses of the triangle inequality in Banach space. J. Inequal. Pure Appl. Math. 6(5), Article ID 139 (2005)
- Rajić, R: Characterization of the norm triangle equality in pre-Hilbert C -modules and applications. J. Math. Inequal. 3, 347-355 (2009)
- Maligranda, L: Simple norm inequalities. Am. Math. Mon. 113, 256-260 (2006)
- Maligranda, L: Some remarks on the triangle inequality for norms. Banach J. Math. Anal. 2, 31-41 (2008)
- Kato, M, Saito, KS, Tamura, T: Sharp triangle inequality and its reverse in Banach spaces. Math. Inequal. Appl. 10, 451-460 (2007)
- Mitani, KI, Saito, KS: On sharp triangle inequalities in Banach spaces II. J. Inequal. Appl. 2010, Article ID 323609 (2010)
- Mineno, K, Nakamura, Y, Ohwada, T: Characterization of the intermediate values of the triangle inequality. Math. Inequal. Appl. 15, 1019-1035 (2012)
- Dadipour, F, Moslehian, MS, Rassias, JM, Takahasi, SE: Characterization of a generalized triangle inequality in normed spaces. Nonlinear Anal. 75, 735-741 (2012)
- Sano, H, Mineno, K, Hirota, Y, Izawa, S, Kimura, C, Ohwada, T: Characterization of the intermediate values of the triangle inequality III. J. Nonlinear Convex Anal. 17, 297-310 (2016)
- Fujii, M, Kato, M, Saito, KS, Tamura, T: Sharp mean triangle inequality. Math. Inequal. Appl. 13, 743-752 (2010)
- Pecarić, J, Rajić, R: The Dunkl-Williams inequality with n elements in normed linear spaces. Math. Inequal. Appl. 10, 461-470 (2007)
- Moszy ńska, M, Richter, WD: Reverse triangle inequality. Antinorms and semi-antinorms. Studia Sci. Math. Hung. 49, 120-138 (2012)
- Fujii, JI, Fujii, M, Seo, Y, Zuo, H: Recent developments of matrix version of the arithmetic-geometric mean inequality. Ann. Funct. Anal. 7(1), 102-117 (2016)
- Djolović, I, Malkowsky, E: Generalization of some results on pα duals. Banach J. Math. Anal. 8(2), 124-130 (2014)
- Dragomir, SS: Upper and lower bounds for the p-angular distance in normed spaces with applications. J. Math. Inequal. 8, 947-961 (2014)
- Dunkl, CF, Williams, KS: A simple norm inequality. Am. Math. Mon. 71, 53-54 (1964)
- Moslehian, MS, Dadipour, F, Rajić, R, Marić, A: A glimpse at the Dunkl-Williams inequality. Banach J. Math. Anal. 5, 138-151 (2011)
- Niculescu, C, Persson, LE: Convex Functions and Their Applications. Springer, New York (2006)
- Ghazanfari, AG, Barani, A: Some Hermite-Hadamard type inequalities for the product of two operator preinvex functions. Banach J. Math. Anal. 9(2), 9-20 (2015)
- Tapia, RA: A characterization of inner product spaces. Proc. Am. Math. Soc. 41, 569-574 (1973)