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.