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Title: On the Convexity of Functions
Authors: Abu-Asa'd, Ata
Hirzallah, omar
Keywords: Unitarily invariant norm;compact operator;positive operator;singular value;, Schatten p-nor;Hilbert-Schmidt norm;convex functions;eigenvalues
Issue Date: 12-Nov-2019
Publisher: Faculty of Sciences and Mathematics, University of Nis, Serbia
Citation: Abu-As'ad, A., & Hirzallah, O. (2019). On the Convexity of Functions. Filomat, 33(2406), 3373–3381.
Series/Report no.: Vol 33, No 12 (2019);3773–3781
Abstract: Let A,B, and X be bounded linear operators on a separable Hilbert space such that A,B are positive, X≥γI, for some positive real number γ, and α∈[0,1]. Among other results, it is shown that if f(t) is an increasing function on [0,∞) with f(0)=0 such that f(√t) is convex, then γ|||f(αA+(1-α)B)+f(β|A-B|)|||≤|||αf(A)X+(1-α)Xf(B)||| for every unitarily invariant norm, where β=min(α,1-α). Applications of our results are given.
Description: This article interest on the relation of matrices under effect of convex function so we make proof of some inequalities study these relation
ISSN: 2406-0933
Appears in Collections:Applied science faculty

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