作者机构：
[Wang, Miao-Kun] Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China.;[Chu, Yu-Ming] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China.;[Zhang, Wen] Icahn Sch Med Mt Sinai, Friedman Brain Inst, New York, NY 10029 USA.
关键词：
Convex function;Csiszár divergence;Jensen’s inequality;s-convex function
摘要：
In the article, we establish an inequality for Csiszár divergence associated with s-convex functions, present several inequalities for Kullback–Leibler, Renyi, Hellinger, Chi-square, Jeffery’s, and variational distance divergences by using particular s-convex functions in the Csiszár divergence. We also provide new bounds for Bhattacharyya divergence.
期刊：
Applied Mathematics and Computation,2019年348:552-564 ISSN：0096-3003
通讯作者：
Chu, Yu-Ming
作者机构：
[Yang, Zhen-Hang] Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China.;[Yang, Zhen-Hang] State Grid Zhejiang Elect Power Res Inst, Customer Serv Ctr, Hangzhou 310009, Zhejiang, Peoples R China.;[Chu, Yu-Ming] Huzhou Univ, Dept Math, Hzhou 313000, Peoples R China.;[Zhang, Wen] Icahn Sch Med Mt Sinai, Friedman Brain Inst, New York, NY 10029 USA.
摘要：
In the article, we prove that the double inequality pi/2J(r') - 51 pi-160/160 r(16) < epsilon(r) < pi/2(r') - 5 pi/3x2(31 )r(16) holds for all r is an element of (0, 1), where epsilon(r) = integral( pi/2)(0)root 1-r(2)sin(2)(t)dt is the complete elliptic integral of the second kind, r' = (1 - r(2))(1/2) and J(r) = 51r(2) + 20r root r + 50r + 20 root r + 51/16(5r + 2 root r + 5). (C) 2018 Elsevier Inc. All rights reserved.
摘要：
We establish a Hermite-Hadamard type identity and several new Hermite-Hadamard type inequalities for conformable fractional integrals and present their applications to special bivariate means.
关键词：
Green's function;Hermite-Hadamard inequality;convex function
摘要：
In the article, we establish the left Riemann-Liouville fractional Hermite-Hadamard type inequalities and the generalized Hermite-Hadamard type inequalities by using Green's function and Jensen's inequality, and present several new Hermite-Hadamard type inequalities for a class of convex as well as monotone functions.
关键词：
Ostrowski inequality;Conformable derivative;Conformable integral;Arithmetic mean;Generalized logarithmic mean
摘要：
In the article, we establish several Ostrowski type inequalities involving the conformable fractional integrals. As applications, we find new inequalities for the arithmetic and generalized logarithmic means.
期刊：
Journal of Mathematical Analysis and Applications,2015年428(1):587-604 ISSN：0022-247X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming; Yang, Zhen-Hang] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Wang, Miao-Kun] Huzhou Univ, Dept Math, Huzhou 813000, Peoples R China.
通讯机构：
[Chu, Yu-Ming] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
关键词：
Quotient of power series;Piecewise monotonicity;Hypergeometric function;Leaden inequality
摘要：
In this paper, we present the necessary and sufficient condition for the monotonicity of the quotient of power series. As applications, some gaps and misquotations in certain published articles are pointed out and corrected, and some known results involving the Landen inequalities for zero-balanced hypergeometric functions are Improved. (C) 2015 Elsevier Inc. All rights reserved.
摘要：
We find the greatest value α
1 and α
2, and the least values β
1 and β
2, such that the double inequalities α
1
S(a,b) + (1 − α
1) A(a,b) < T(a,b) < β
1
S(a,b) + (1 − β
1) A(a,b) and
$S^{\alpha_{2}}(a,b)A^{1-\alpha_{2}}(a,b)< T(a,b)< S^{\beta_{2}}(a,b)A^{1-\beta_{2}}(a,b)$
hold for all a,b > 0 with a ≠ b. As applications, we get two new bounds for the complete elliptic integral of the second kind in terms of elementary functions. Here, S(a,b) = [(a
2 + b
2)/2]1/2, A(a,b) = (a + b)/2, and
$T(a,b)=\frac{2}{\pi}\int\limits_{0}^{{\pi}/{2}}\sqrt{a^2{\cos^2{\theta}}+b^2{\sin^2{\theta}}}{\rm d}\theta$
denote the root-square, arithmetic, and Toader means of two positive numbers a and b, respectively.
