Inverses of Operator Convex Functions

2016 ◽  
pp. 363-370 ◽  
Author(s):  
Henrik L. Pedersen ◽  
Mitsuru Uchiyama
Keyword(s):  
Convex Functions ◽  
Operator Convex ◽  
Operator Convex Functions

scholarly journals Some Hermite-Hadamard type inequalities for operator convex functions and positive maps

2019 ◽  
Vol 7 (1) ◽  
pp. 38-51 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Power Function ◽  
Convex Functions ◽  
Positive Maps ◽  
Operator Convex ◽  
Operator Convex Functions

Abstract In this paper we establish some inequalities of Hermite-Hadamard type for operator convex functions and positive maps. Applications for power function and logarithm are also provided.

Cyclic Refinements of the Different Versions of Operator Jensen's Inequality

2016 ◽  
Vol 31 ◽  
pp. 125-133 ◽  
Author(s):  
Laszlo Horvath ◽  
Khuram Khan ◽  
Josip Pecaric
Keyword(s):  
Convex Functions ◽  
Jensen’S Inequality ◽  
Jensen's Inequality ◽  
Norm Inequalities ◽  
Power Means ◽  
Operator Convex ◽  
Operator Convex Functions

Refinements of the operator Jensen's inequality for convex and operator convex functions are given by using cyclic refinements of the discrete Jensen's inequality. Similar refinements are fairly rare in the literature. Some applications of the results to norm inequalities, the Holder McCarthy inequality and generalized weighted power means for operators are presented.

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