A New Type of Operator Convexity
A New Type of Operator Convexity
Source title:
Acta Mathematica Vietnamica, 43(4): 595-605,
2018
(Scopus)
Academic year of acceptance:
2018-2019
Abstract:
Let r, s be positive numbers. We define a new class of operator (r, s) -convex functions by the following inequality
f ([λAr+(1−λ)Br]1/r)≤[λf(A)s+(1−λ) f(B)s]1/s,
where A, B are positive definite matrices and for any λ∈[0,1] . We prove the Jensen, Hansen-Pedersen, and Rado type inequalities for such functions. Some equivalent conditions for a function f to become operator (r, s) -convex are established.