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DUNKL–WILLIAMS INEQUALITIES FOR INTEGRABLE FUNCTIONS IN BANACH SPACE

Published online by Cambridge University Press:  12 December 2012

JIANBING CAO
JIANBING CAO*
Affiliation:
Department of Mathematics, East China Normal University, Dongchuan RD 500, Shanghai 200241, PR China Department of Mathematics, Henan Institute of Science and Technology, Xinxiang, Henan 453003, PR China email caocjb@163.com
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Abstract

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In this paper, a generalisation of the Dunkl–Williams inequality is established for strongly integrable functions with values in a Banach space. Some applications are also presented.

Keywords

Dunkl–Williams inequalitytriangle inequalityBanach space
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 2 , April 2013 , pp. 298 - 303
Copyright
Copyright ©2012 Australian Mathematical Publishing Association Inc.

References

Dadipour, F., Moslehian, M. S., Rassias, J. M. and Takahasi, S.-E., ‘Characterization of a generalized triangle inequality in normed spaces’, Nonlinear Anal. 75 (2) (2012), 735–741.CrossRefGoogle Scholar
Dragomir, S. S., ‘Reverses of the triangle inequality in Banach spaces’, J. Inequal. Pure Appl. Math. 6 (5) (2005), 46; Art. 129.Google Scholar
Dragomir, S. S., ‘Reverses of the continuous triangle inequality for Bochner integral in complex Hilbert spaces’, J. Math. Anal. Appl. 329 (1) (2007), 65–76.CrossRefGoogle Scholar
Dunkl, C. F. and Williams, K. S., ‘A simple norm inequality’, Amer. Math. Monthly. 71 (1964), 53–54.CrossRefGoogle Scholar
Hsu, C.-Y., Shaw, S.-Y. and Wong, H.-J., ‘Refinements of generalized triangle inequalities’, J. Math. Anal. Appl. 344 (2008), 613–639.CrossRefGoogle Scholar
Kato, M., Saito, K.-S. and Tamura, T., ‘Sharp triangle inequality and its reverse in Banach space’, Math. Inequal. Appl. (2007), 451–460.Google Scholar
Maligranda, L., ‘Simple norm inequalities’, Amer. Math. Monthly. 133 (2006), 256–260.CrossRefGoogle Scholar
Mercer, P. R., ‘The Dunkl–Williams inequality in an inner-product space’, Math. Inequal. Appl. 10 (2007), 447–451.Google Scholar
Pec˘aric˘, J. and Rajic˘, R., ‘The Dunkl–Williams inequality with $n$ elements in normed linear spaces’, Math. Inequal. Appl. 10 (2007), 461–470.Google Scholar
Pec˘aric˘, J. and Rajic˘, R., ‘The Dunkl–Williams equality in pre-Hilbert ${C}^{\ast } $-modules’, Linear. Algebra. Appl. 425 (2007), 16–25.Google Scholar
Takahasi, S.-E., Rassias, J. M., Saitoh, S. and Takahashi, Y., ‘Refined generalizations of the triangle inequality on Banach spaces’, Math. Inequal. Appl. 13 (4) (2010), 733–741.Google Scholar