Some inequalities for operator (p, h)-convex functions

Let p be a positive number and h a function on satisfying for any . A non-negative continuous function f on is said to be operator (p, h)-convex if holds for all positive semidefinite matrices A, B of order n with spectra in K, and for any . In this paper, we study properties of operator (p, h)-conv...

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Bibliographic Details
Published in:Linear & multilinear algebra Vol. 66; no. 3; pp. 580 - 592
Main Authors: Dinh, Trung Hoa, Vo, Khue Thi Bich
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 04.03.2018
Taylor & Francis Ltd
Subjects:
Continuity (mathematics)
Convex analysis
h)-convex functions
Inequalities
Mathematical analysis
Matrix methods
Monotone functions
Operator (p
operator Hansen-Pedersen type inequality
operator Jensen type inequality
Operators (mathematics)
ISSN:0308-1087, 1563-5139
Online Access:Get full text
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Summary:Let p be a positive number and h a function on satisfying for any . A non-negative continuous function f on is said to be operator (p, h)-convex if holds for all positive semidefinite matrices A, B of order n with spectra in K, and for any . In this paper, we study properties of operator (p, h)-convex functions and prove the Jensen, Hansen-Pedersen type inequalities for them. We also give some equivalent conditions for a function to become an operator (p, h)-convex. In applications, we obtain Choi-Davis-Jensen type inequality for operator (p, h)-convex functions and a relation between operator (p, h)-convex functions with operator monotone functions.
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content type line 14
ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2017.1307914