Vector joint majorization and generalization of Csiszár–Körner’s inequality for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.gif" display="inline" overflow="scroll"><mml:mi>f</mml:mi></mml:math>-divergence

Niezgoda, Marek

doi:10.1016/j.dam.2015.06.018

Cited by 13 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Sherman's result has attracted the interest of several mathematicians (see [1][2][3][4][5], [12][13][14][15], [23][24][25][26][27][28][29][30]).…”

Section: ) We Get Majorization Inequalitymentioning

confidence: 99%

Sherman’s inequality and its converse for strongly convex functions withapplications to generalizedf-divergences

Bradanovic¹

2019

Turk J Math

View full text Add to dashboard Cite

Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n -strongly convex functions using extended idea of convexity to the class of strongly convex functions. We also obtain upper bound for Sherman's inequality, called the converse Sherman inequality, and as easy consequences we get Jensen's as well as majorization inequality and their conversions for strongly convex functions. Obtained results are stronger versions for analogous results for convex functions. As applications, we introduced a generalized concept of f -divergence and derived some reverse relations for such concept.

show abstract

“…Recently, Sherman's result has attracted the interest of several mathematicians (see [1][2][3][4][5], [12][13][14][15], [23][24][25][26][27][28][29][30]).…”

Section: ) We Get Majorization Inequalitymentioning

confidence: 99%

Sherman’s inequality and its converse for strongly convex functions withapplications to generalizedf-divergences

Bradanovic¹

2019

Turk J Math

View full text Add to dashboard Cite

show abstract

“…The reader is referred to [15] for applications of Sherman inequality. The first example is to show the merits of Sherman inequality (3).…”

Section: Introductionmentioning

confidence: 99%

Sherman, Hermite-Hadamard and Fejér like inequalities for convex sequences and nondecreasing convex functions

Niezgoda

2017

Filomat

Self Cite

View full text Add to dashboard Cite

In this paper, we prove Sherman like inequalities for convex sequences and nondecreasing convex functions. Thus we develop some results by S. Wu and L. Debnath [19]. In consequence, we derive discrete versions for convex sequences of Petrovic and Giaccardi?s inequalities. As applications, we establish some generalizatons of Fej?r inequality for convex sequences. We also study inequalities of Hermite-Hadamard type. Thus we extend some recent results of Latreuch and Bela?di [8]. In our considerations we use some matrix methods based on column stochastic and doubly stochastic matrices.

show abstract

“…Statement (1.4) is referred to as Sherman's inequality. (Some applications of Theorem B can be found in [1], [10], and [11]. )…”

Section: Introductionmentioning

confidence: 99%

Sherman type theorem on $C^{\ast}$ -algebras

Niezgoda¹

2017

Ann. Funct. Anal.

View full text Add to dashboard Cite

In this paper, a new definition of majorization for C * -algebras is introduced. Sherman's inequality is extended to self-adjoint operators and positive linear maps by applying the method of premajorization used for comparing two tuples of objects. A general result in a matrix setting is established. Special cases of the main theorem are studied. In particular, a HLPK-type inequality is derived. m i=1 s ij = 1 for j = 1, . . . , n. An m × n real matrix S = (s ij ) is called row-stochastic if s ij ≥ 0 for i = 1, . . . , m, j = 1, . . . , n, and all row sums of S are

show abstract

Vector joint majorization and generalization of Csiszár–Körner’s inequality forf-divergence

Cited by 13 publications

References 9 publications

Sherman’s inequality and its converse for strongly convex functions withapplications to generalizedf-divergences

Sherman’s inequality and its converse for strongly convex functions withapplications to generalizedf-divergences

Sherman, Hermite-Hadamard and Fejér like inequalities for convex sequences and nondecreasing convex functions

Sherman type theorem on $C^{\ast}$ -algebras

Contact Info

Product

Resources

About