On a Generalization of a Complementary Triangle Inequality in Hilbert Spaces and Banach Spaces

被引：0
作者：
Debmalya Sain
机构：
[1] Indian Institute of Science,Department of Mathematics
来源：
Indian Journal of Pure and Applied Mathematics | 2020年 / 51卷
关键词：
Triangle inequality; convexity; normed spaces; inner product spaces; 46B20; 47A30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study a possible generalization of a complementary triangle inequality in Hilbert spaces and Banach spaces. Our results in the present article improve and generalize some of the earlier results in this context. We also present an operator norm inequality in the setting of Banach spaces, as an application of the present study.
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页码：1815 / 1827
页数：12
相关论文
共 17 条
[1]  
Diaz J B(1964)Complementary inequalities. I: Inequalities complementary to Cauchy’s inequality for sums of real numbers J. Math. Anal. appl. 9 278-293
[2]  
Metcalf F T(1966)A complementary triangle inequality in Hilbert and Banach spaces Proc. Amer. Math. Soc. 17 88-97
[3]  
Diaz J B(1967)Classes of semi-inner-product spaces Trans. Amer. Math. Soc. 129 436-446
[4]  
Metcalf F T(1961)Semi-inner-product spaces Trans. Amer. Math. Soc. 100 29-43
[5]  
Giles J R(2019)Reverses of the triangle inequality for absolute value in Hilbert Ital. J. Pure Appl. Math. 41 262-273
[6]  
Lumer G(2005)-modules Linear Algebra Appl. 402 245-254
[7]  
Mansoori A(2018)Some reverses of the generalised triangle inequality in complex inner product spaces J. Operator Theorey 80 399-413
[8]  
Omidvar M E(2013)A complete characterization of Birkhoff-James orthogonality in infinite dimensional normed space Linear Algebra Appl. 439 2448-2452
[9]  
Moradi H R(1963)Operator norm attainment and inner product spaces Proc. Amer. Math. Soc. 14 263-265
[10]  
Dragomir S S(undefined)Some applications of the inequality of arithmetic and geometric means to polynomial equations undefined undefined undefined-undefined
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