Geodesic
Convexity and inequalities of some generalized numerical radius functions
Filomat, Tome 36 (2022) no. 5, p. 1649

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DOI

In this paper, we prove that each of the following functions is convex on R : f (t) = w N (A t XA 1−t ± A 1−t XA t), (t) = w N (A t XA 1−t), and h(t) = w N (A t XA t) where A > 0, X ∈ M n and N(.) is a unitarily invariant norm on M n. Consequently, we answer positively the question concerning the convexity of the function t → w(A t XA t) proposed by in (2018). We provide some generalizations and extensions of w N (.) by using Kwong functions. More precisely, we prove the following w N (f (A)X(A) + (A)X f (A)) ≤ w N (AX + XA) ≤ 2w N (X)N(A), which is a kind of generalization of Heinz inequality for the generalized numerical radius norm. Finally, some inequalities for the Schatten p-generalized numerical radius for partitioned 2 × 2 block matrices are established, which generalize the Hilbert-Schmidt numerical radius inequalities given by Aldalabih and Kittaneh in (2019).
DOI : 10.2298/FIL2205649A
Classification : 47A12;47A30, 47A63, B15, B47
Keywords: Schatten p-generalized numerical radius, Convexity, Kwong function, Matrix norm inequalities 
Hassane Abbas; Sadeem Harb; Hassan Issa. Convexity and inequalities of some generalized numerical radius functions. Filomat, Tome 36 (2022) no. 5, p. 1649 . doi: 10.2298/FIL2205649A
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     title = {Convexity and inequalities of some generalized numerical radius functions},
     journal = {Filomat},
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     year = {2022},
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     doi = {10.2298/FIL2205649A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2205649A/}
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