Uniform convexity, strong convexity and property UC
نویسندگان
چکیده
منابع مشابه
Convexity Property and Applications
We extend to infinite dimensional separable Hilbert spaces the Schur convexity property 13 of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of linear selfadjoint operators 15 that can be approximated by operators of finite rank and having a countable family of eigenvalues. The abstract results of the...
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The standard proof of the uniform convexity of L using Clarkson’s [1] or Hanner’s [2] inequalities (see also [4]) is rarely taught in functional analysis classes, in part (the author imagines) because the proofs of those inequalities are quite non-intuitive and unwieldy. We present here a direct proof, cheerfully sacrificing the optimal bounds – for which, see [2, 4]. It fits quite nicely in wi...
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In this paper, strongly (α ,T ) -convex functions, i.e., functions f : D → R satisfying the functional inequality f (tx+(1− t)y) t f (x)+(1− t) f (y)− tα(1− t)(x− y)− (1− t)αt(y− x) for x,y ∈ D and t ∈ T ∩ [0,1] are investigated. Here D is a convex set in a linear space, α is a nonnegative function on D−D , and T ⊆ R is a nonempty set. The main results provide various characterizations of stron...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2017
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2016.10.001