A variant of the Jensen–Mercer operator inequality for superquadratic functions

Barić, Josipa; Matković, Anita; Pečarić, Josip

doi:10.1016/j.mcm.2010.01.005

Cited by 14 publications

(8 citation statements)

References 2 publications

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“…Regarding operator extensions of the classical results, we proved a variant of the Jensen inequality for superquadratic functions involving operators in [15]. The authors of [8] presented some Mercer type operator inequalities for superquadratic functions. Regarding Mercer inequality, E. Anjdani [5] gave another variant and also presented some reverse results in [6].…”

Section: Introductionmentioning

confidence: 97%

Inequalities Involving Superquadratic Functions and Operators

Kian

Dragomir

2013

Mediterr. J. Math.

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There exist two major subclasses in the class of superquadratic functions, one contains concave and decreasing functions and the other, contains convex and monotone increasing functions. We use this fact and present eigenvalue inequalities in each case. The nature of these functions enables us to apply our results in two directions. First improving some known results concerning eigenvalues for convex functions and second, obtaining some complimentary inequalities for some other functions. We will give some examples to support our results as well. As applications, some subadditivity inequalities for matrix power functions have been presented. In particular, if X and Y are positive matrices, thenfor some unitaries U, V ∈ M n .

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Section: Introductionmentioning

confidence: 97%

Inequalities Involving Superquadratic Functions and Operators

Kian

Dragomir

2013

Mediterr. J. Math.

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“…For more details about superquadratic functions, including various examples, properties, and diverse applications in the theory of inequalities, the reader is referred to [2,3,6,7,8,10,18,21] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

On logarithmically superquadratic functions

Krnić

Moradi

Sababheh

2023

Preprint

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In this paper, we develop a concept of a logarithmically super\-qua\-dratic function. Such a class of functions is defined via superquadratic functions.These functions possess some superior properties, especially if they take values greater than or equal to one. We prove that they are convex and superadditive in the latter case.In particular, we also obtain the corresponding refinement of the Jensen inequality in a product form. Furthermore, we derive an external form of the Jenseninequality and the corresponding reverse. Finally, we give a variant of the Jensen operator inequality for logarithmically superquadratic functions.All established results are derived via the corresponding relations for superquadratic functions.

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“…Mercer. It has been a main topic of our research (see, e.g., [4][5][6][7]) in different settings and for different classes of functions.…”

Section: Introductionmentioning

confidence: 99%