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On Hanner type inequalities with a weight for Banach spaces |
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| Authors: | Yasutaka Yamada Mikio Kato |
| Institution: | a Kitakyushu College of Technology, Kitakyushu 802-0985, Japan b Department of System Engineering, Okayama Prefectural University, Soja 719-1197, Japan c Department of Mathematics, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan |
| Abstract: | We shall present several Hanner type inequalities with a weight constant and characterize 2-uniformly smooth and 2-uniformly convex Banach spaces with these inequalities. p-Uniformly smooth and q-uniformly convex Banach spaces will be also characterized with another Hanner type inequalities with a weight in the other side term. The best value of the weight in these inequalities will be determined for Lp spaces. Also we shall present a duality theorem between these inequalities in a generalized form. |
| Keywords: | Hanner's inequality Hanner type inequality with a weight p-Uniformly smooth Banach space q-Uniformly convex Banach space Duality Best weight constant for _method=retrieve& _eid=1-s2 0-S0022247X05013600& _mathId=si2 gif& _pii=S0022247X05013600& _issn=0022247X& _acct=C000053510& _version=1& _userid=1524097& md5=ee166e40d6600d5b87d4eca8c5e29503')" style="cursor:pointer Lp" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">Lp |
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