Geodesic
New inequalities for (p, h)-convex functions for τ-measurable operators
Filomat, Tome 37 (2023) no. 16, p. 5259

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DOI

The main goal of this article is to present new inequalities for (p, h)-convex and (p, h) log-convex functions for a non-negative super-multiplicative and super-additive function h. Our first main result will be hλ ( v µ ) ≤ (h(1 − v) f (a) + h(v) f (b))λ − f λ [ ((1 − v)ap + vbp) 1p ] (h(1 − µ) f (a) + h(µ) f (b))λ − f λ [ ((1 − µ)ap + µbp) 1p ] ≤ hλ ( 1 − v 1 − µ ) , for the positive (p, h)-convex function f ,when λ ≥ 1, p ∈ R\{0} and 0 ≤ v ≤ µ ≤ 1. This gives a generalization of an important result due to M. Sababheh [Linear Algebra Appl. 506 (2016), 588–602]. As applications of our results, we present many inequalities for the trace, and the symmetric norms for τ-measurable operators.
DOI : 10.2298/FIL2316259I
Classification : 15A39, 15B48, 26D15, 15A60
Keywords: (p, h)-convex function, Operator (p, h)-convex function, τ-measurable operators, Super-additive functions, Multiplicative functions 
Mohamed Amine Ighachane; Mohammed Bouchangour. New inequalities for (p, h)-convex functions for τ-measurable operators. Filomat, Tome 37 (2023) no. 16, p. 5259 . doi: 10.2298/FIL2316259I
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     title = {New inequalities for (p, h)-convex functions for \ensuremath{\tau}-measurable operators},
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     year = {2023},
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     doi = {10.2298/FIL2316259I},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2316259I/}
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