A Refinement of Jensen's Inequality for a Class of Increasing and Concave Functions
Suppose that f(x) is strictly increasing, strictly concave, and twice continuously differentiable on a nonempty interval I__, and f_(x) is strictly convex on I. Suppose that xk_[a,b]_I, where 0<a<b, and pk_0 for k=1,_,n, and suppose that _k=1npk=1. Let x_=_k=1npkxk, and _2=_k=1npk(xk_x_)2. We...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2008-07-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2008/717614 |