• The Pure and Applied Mathematics
• /
• v.29 no.1
• /
• pp.51-57
• /
• 2022

The Jensen, Simic and Mercer inequalities are very important inequalities in theory of inequalities and some results are devoted to this inequalities. In this paper, firstly, we establish extension of Jensen-Simic-Mercer inequality. After that, we investigate bounds for Shannons entropy of a probability distribution. Finally, We give some new applications in analysis.

• Journal of the Korean Mathematical Society
• /
• v.45 no.3
• /
• pp.821-834
• /
• 2008

Refinements of a variant of Jensen's inequality for functions with nondecreasing increments are presented. Obtained results are used to prove refinements of related variants of Cebysev's inequality and Holder's inequality.

• Honam Mathematical Journal
• /
• v.44 no.4
• /
• pp.513-520
• /
• 2022

The Jensen and Mercer inequalities are very important inequalities in information theory. The article provides the generalization of Mercer's inequality for convex functions on the line segments. This result contains Mercer's inequality as a particular case. Also, we investigate bounds for Shannon's entropy and give some new applications in zeta function and analysis.

• Kyungpook Mathematical Journal
• /
• v.52 no.4
• /
• pp.495-511
• /
• 2012

In this paper, we prove some inequalities in terms of G$\hat{a}$teaux derivatives for convex functions defined on linear spaces and also give improvement of Jensen's inequality. Furthermore, we give applications for norms, mean $f$-deviations and $f$-divergence measures.

• Journal of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.465-477
• /
• 2013

In this paper, two different methods of proving Jensen's inequality on time scales for superquadratic functions are demonstrated. Some refinements of classical inequalities on time scales are obtained using properties of superquadratic functions and some known results for isotonic linear functionals.

• Honam Mathematical Journal
• /
• v.45 no.1
• /
• pp.123-129
• /
• 2023

In this paper, we introduce the reverse of the operator Davis-Choi-Jensen's inequality. Our results are employed to establish a new bound for the Furuta inequality. More precisely, we prove that, if $A,\;B{\in}{\mathcal{B}}({\mathcal{H}})$ are self-adjoint operators with the spectra contained in the interval [m, M] with m < M and A ≤ B, then for any $r{\geq}{\frac{1}{t}}>1,\,t{\in}(0,\,1)$ $A^r{\leq}({\frac{M1_{\mathcal{H}}-A}{M-m}}m^{rt}+{\frac{A-m1_{\mathcal{H}}}{M-m}}M^{rt}){^{\frac{1}{t}}}{\leq}K(m,\;M,\;r)B^r,$ where K (m, M, r) is the generalized Kantorovich constant.

• The Pure and Applied Mathematics
• /
• v.19 no.3
• /
• pp.305-313
• /
• 2012

In this note we study Nesbitt's Inequality and modify it to make several inequalities. We prove some inequalities by using power series and Cauchy-Schwarz Inequality.

• Honam Mathematical Journal
• /
• v.44 no.3
• /
• pp.360-369
• /
• 2022

The aim of this study is to establish some new Jensen and Lazhar type inequalities for p-convex function that is a generalization of convex and harmonic convex functions. The results obtained here are reduced to the results obtained earlier in the literature for convex and harmonic convex functions in special cases.

• Journal of the Korean Mathematical Society
• /
• v.45 no.2
• /
• pp.513-525
• /
• 2008

Using known properties of superquadratic functions we obtain a sequence of inequalities for superquadratic functions such as the Converse and the Reverse Jensen type inequalities, the Giaccardi and the Petrovic type inequalities and Hermite-Hadamard's inequalities. Especially, when the superquadratic function is convex at the same time, then we get refinements of classical known results for convex functions. Some other properties of superquadratic functions are also given.

• Communications of the Korean Mathematical Society
• /
• v.31 no.1
• /
• pp.95-100
• /
• 2016

In this paper, we establish a new refinement of the arithmetic-geometric mean inequality. Applying this result in information theory, we obtain a more precise upper bound for Shannon's entropy.