期刊：
JOURNAL OF MATHEMATICAL INEQUALITIES,2013年7(3):349-355 ISSN：1846-579X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Wang, Miao-Kun] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.;[Ma, Xiao-Yan; Qiu, Ye-Fang] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310018, Zhejiang, 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：
Geometric mean;logarithmic mean;arithmetic-geometric mean of Gauss;arithmetic mean
摘要：
For fixed s >= 1 and t(1), t(2) is an element of (0,1/2) we prove that the inequalities G(s)(t(1)a+(1 - t(1))b, t(1)b+(1-t(1))a)A(1-s)(a,b) > AG(a,b) and G(s)(t(2)a+(1-t(2)) b,t(2)b+(1-t(2))a)A(1-s)(a,b) > L(a,b) hold for all a, b > 0 with a not equal b if and only if t(1) >= 1/2-root 2s/(4s) and t2 >= 1/2-root 6s/(6s). Here G(a,b), L(a,b), A(a,b) and AG(a,b) are the geometric, logarithmic, arithmetic and arithmetic- geometric means of a and b, respectively.
期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2013年2013(1):1-13 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming; Song, Ying-Qing; Gong, Wei-Ming] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Long, Bo-Yong] Anhui Univ, Coll Math Sci, Hefei 230039, 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：
generalized logarithmic mean;Neuman-Sandor mean;first Seiffert mean;second Seiffert mean
摘要：
In this paper, we prove three sharp inequalities as follows:
,
and
for all
with
. Here,
,
,
and
are the r th generalized logarithmic, Neuman-Sándor, first and second Seiffert means of a and b, respectively. MSC:26E60.
期刊：
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY,2013年70(2):645-649 ISSN：0340-6253
通讯作者：
Zeng, Ting
作者机构：
[Zeng, Ting; Zeng, T] Hunan City Univ, Coll Math & Comp Sci, Yiyang City 413000, Hunan, Peoples R China.
通讯机构：
[Zeng, Ting] H;Hunan City Univ, Coll Math & Comp Sci, Yiyang City 413000, Hunan, Peoples R China.
摘要：
The Harary index is defined as the sum of reciprocal distances between all pairs of vertices in a nontrivial connected graph. All established results on Harary index mainly deal with bounds and extremal properties of Harary index. In this paper, we give a new sufficient condition, in terms of Harary index, for a connected bipartite graph to be Hamiltonian.
作者机构：
[Zeng, Ting; Zeng, T] Hunan City Univ, Coll Math & Comp Sci, Yiyang City 413000, Hunan, Peoples R China.
通讯机构：
[Zeng, Ting] H;Hunan City Univ, Coll Math & Comp Sci, Yiyang City 413000, Hunan, Peoples R China.
关键词：
Degree;Eccentricity;SSE;M-1-index;chemical tree
摘要：
The sum of the squares of eccentricity (SSE), also called the first normalized Zagreb eccentricity index. In [D. Vukičević et al. [J. Math. Chem. 48, No. 2, 370–380 (2010; Zbl 1196.92050)], the authors compared the first and second normalized Zagreb eccentricity indices for trees and unicyclic graphs. In this paper, we study the problem of comparing the sum of square of eccentricity with the sum of square of degree (also called the first Zagreb index (M 1 -index)). We prove that SSE is always greater than M 1 -index for any chemical tree with at least three vertices, other than an exception. Moreover, we compare SSE with M 1 -index for two classes of connected graphs.
摘要：
In the paper, the authors prove that the generalized sine function sin(p,q) x and the generalized hyperbolic sine function sinh(p,q) x are respectively geometrically concave and geometrically convex. Consequently, the authors verify a conjecture posed by B. A. Bhayo and M. Vuorinen. (c) 2013 Elsevier Inc. All rights reserved.
期刊：
Abstract and Applied Analysis,2013年2013:1-5 ISSN：1085-3375
通讯作者：
Chu, Yu-Ming
作者机构：
[He, Zai-Yin] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China.;[Qian, Wei-Mao] Huzhou Broadcast & TV Univ, Sch Distance Educ, Huzhou 313000, Peoples R China.;[Jiang, Yun-Liang] Huzhou Teachers Coll, Sch Informat & Engn, Huzhou 313000, Peoples R China.;[Chu, Yu-Ming; Song, Ying-Qing] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, 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：
We give the greatest values r 1;r 2 and the least values s 1;s 2 in (1/2;1) such that the double inequalities C ( r 1 a + ( 1 - r 1 ) b;r 1 b + ( 1 - r 1 ) a ) < α A ( a;b ) + ( 1 - α ) T ( a;b ) < C ( s 1 a + ( 1 - s 1 ) b;s 1 b + ( 1 - s 1 ) a ) and C ( r 2 a + ( 1 - r 2 ) b;r 2 b + ( 1 - r 2 ) a ) < α A ( a;b ) + ( 1 - α ) M ( a;b ) < C ( s 2 a + ( 1 - s 2 ) b;s 2 b + ( 1 - s 2 ) a ) hold for any α ∈ ( 0;1 ) and all a;b > 0 with a ≠ b;where A ( a;b );M ( a;b );C ( a;b );and T ( a;b ) are the arithmetic;Neuman-Sándor;contraharmonic;and second Seiffert means of a and b;respectively. Published: 2013 First available in Project Euclid: 27 February 2014 zbMATH: 1272.26030 MathSciNet: MR3035386 Digital Object Identifier: 10.1155/2013/903982
摘要：
We give the greatest values r 1 , r 2 and the least values s 1 , s 2 in (1/2, 1) such that the double inequalities C ( r 1 a + ( 1 - r 1 ) b , r 1 b + ( 1 - r 1 ) a ) < α A ( a , b ) + ( 1 - α ) T ( a , b ) < C ( s 1 a + ( 1 - s 1 ) b , s 1 b + ( 1 - s 1 ) a ) and C ( r 2 a + ( 1 - r 2 ) b , r 2 b + ( 1 - r 2 ) a ) < α A ( a , b ) + ( 1 - α ) M ( a , b ) < C ( s 2 a + ( 1 - s 2 ) b , s 2 b + ( 1 - s 2 ) a ) hold for any α ∈ ( 0,1 ) and all a , b > 0 with a ≠ b , where A ( a , b ) , M ( a , b ) , C ( a , b ), and T ( a , b ) are the arithmetic, Neuman-Sándor, contraharmonic, and second Seiffert means of a and b , respectively.
摘要：
In this work, a class of fuzzy Cohen-Grossberg neural networks (fcgnns) with time-varying delays and impulse are considered. Applying differential inequality techniques, some sufficient conditions for the existence, uniqueness and global exponential stability of equilibrium point for the addressed neural network are obtained. Moreover an example illustrates the effectiveness of obtained results.
期刊：
JOURNAL OF MATHEMATICAL INEQUALITIES,2013年7(4):659-668 ISSN：1846-579X
通讯作者：
Chu, Yuming
作者机构：
[Chu, Yuming] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Liu, Baoyu] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China.;[Wang, Miaokun] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China.
通讯机构：
[Chu, Yuming] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
关键词：
First Seiffert means;second Seiffert mean;harmonic mean;arithmetic mean;quadratic mean
摘要：
In this paper, we find the greatest values alpha, lambda and the least values beta, mu such that the double inequalities alpha[5A(a, b)/6 + H(a, b)/6] + (1 - alpha)A(5/6)(a, b)H-1/6(a, b) < P(a, b) < beta[5A(a, b)/6 + H(a, b)/6]+(1-beta)A(5/6) (a, b)H-1/6(a, b) and lambda[A(a, b)/3 + 2Q(a,b)/3]+(1 - lambda)A(1/3) (a, b)Q(2/3)(a, b) < T(a, b) < mu[A(a, b)/3 + 2Q(a, b)/3]+(1 - mu)A(1/3)(a, b)Q(2/3)(a, b) hold for all a,b > 0 with a not equal b. Here A(a, b), H(a, b), Q(a, b), P(a, b) and T(a, b) denote the arithmetic, harmonic, quadratic, first Seiffert and second Seiffert means of two positive numbers a and b, respectively.
摘要：
In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl.
56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by using the bifurcation method (Feng et al, Appl. Math. Comput.
189, 271 (2007); Li et al, Appl. Math. Comput.
175, 61 (2006)).
摘要：
This paper is devoted to the existence of compressible liquid crystals system in non-smooth domain. We are tempted to prove the convergence of solutions depending on that of corresponding spatial domains for liquid crystals equations of compressible flow. Copyright (c) 2012 John Wiley & Sons, Ltd.
期刊：
Journal of Applied Mathematics,2013年2013(Pt.9):582504:1-582504:7 ISSN：1110-757X
通讯作者：
Chu, Yu-Ming
作者机构：
[Zhang, Fan] Huzhou Vocat & Tech Coll, Sch Architecture Engn, Huzhou 313000, Peoples R China.;[Chu, Yu-Ming] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Qian, Wei-Mao] Huzhou Broadcast & TV Univ, Dept Distance Educ, Huzhou 313000, 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：
We present the largest values α1;and α3 and the smallest values β1;and β3 such that the double inequalities α1M(a;b)+(1-α1)H(a;b)0 with a≠b;where M(a;b);A(a;b);He(a;b);H(a;b) and H-(a;b) denote the Neuman-Sándor;arithmetic;Heronian;harmonic;and harmonic root-square means of a and b;respectively. Published: 2013 First available in Project Euclid: 14 March 2014 zbMATH: 06950758 MathSciNet: MR3147875 Digital Object Identifier: 10.1155/2013/582504
摘要：
We present the largest values alpha(1), alpha(2), and alpha(3) and the smallest values beta(1), beta(2), and beta(3) such that the double inequalities alpha M-1(a,b) + (1 alpha(1))H(a,b) < A(a,b) < beta M-1(a,b) + (1 beta(1))H(a,b), alpha M-2(a,b) + (1 alpha(2))(H) over bar (a,b) < A(a,b) < beta M-2(a,b) + ( 1 beta(2))(H) over bar (a,b), and alpha M-3(a,b) + (1 - alpha(3))He(a,b) < A(a,b) < beta M-3(a,b) + (1 - beta(3))He(a,b) hold for all a,b > 0 with a not equal b, where M(a,b), A(a,b), He(a,b), H(a,b) and (H) over bar (a,b) denote the Neuman-Sandor, arithmetic, Heronian, harmonic, and harmonic root-square means of a and b, respectively.
期刊：
Abstract and Applied Analysis,2013年2013:1-12 ISSN：1085-3375
通讯作者：
Chu, Yu-Ming
作者机构：
[Zhao, Tie-Hong] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China.;[Chu, Yu-Ming] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Jiang, Yun-Liang] Huzhou Teachers Coll, Sch Informat & Engn, Huzhou 313000, Peoples R China.;[Li, Yong-Min] Southeast Univ, Sch Automat, Nanjing 210096, Jiangsu, 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：
We prove that the double inequalities I α 1 ( a;b ) Q 1 - α 1 ( a;b ) < M ( a;b ) < I β 1 ( a;b ) Q 1 - β 1 ( a;b );I α 2 ( a;b ) C 1 - α 2 ( a;b ) < M ( a;b ) < I β 2 ( a;b ) C 1 - β 2 ( a;b ) hold for all a;b > 0 with a ≠ b if and only if α 1 ≥ 1 / 2;β 1 ≤ log [ 2 log ( 1 + 2 ) ] / ( 1 - log 2 );and β 2 ≤ log [ 2 log ( 1 + 2 ) ];where I ( a;b );M ( a;b );Q ( a;b );and C ( a;b ) are the identric;Neuman-Sándor;quadratic;and contraharmonic means of a and b;respectively. Published: 2013 First available in Project Euclid: 27 February 2014 zbMATH: 1276.26065 MathSciNet: MR3035385 Digital Object Identifier: 10.1155/2013/348326
摘要：
We prove that the double inequalities I α 1 ( a , b ) Q 1 - α 1 ( a , b ) < M ( a , b ) < I β 1 ( a , b ) Q 1 - β 1 ( a , b ) , I α 2 ( a , b ) C 1 - α 2 ( a , b ) < M ( a , b ) < I β 2 ( a , b ) C 1 - β 2 ( a , b ) hold for all a , b > 0 with a ≠ b if and only if α 1 ≥ 1 / 2 , β 1 ≤ log [ 2 log ( 1 + 2 ) ] / ( 1 - log 2 ) , α 2 ≥ 5 / 7 , and β 2 ≤ log [ 2 log ( 1 + 2 ) ] , where I ( a , b ) , M ( a , b ) , Q ( a , b ) , and C ( a , b ) are the identric, Neuman-Sándor, quadratic, and contraharmonic means of a and b , respectively.
期刊：
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY,2013年39(2):259-269 ISSN：1017-060X
通讯作者：
Chu, Y. M.
作者机构：
[Chu, Y. M.; Hou, S. W.] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Hunan, Peoples R China.;[Xia, W. F.] Huzhou Teachers Coll, Sch Teacher Educ, Huzhou 313000, Zhejiang, Peoples R China.
通讯机构：
[Chu, Y. M.] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Hunan, Peoples R China.
关键词：
Centroidal mean;Harmonic mean;Identric mean;Logarithmic mean
摘要：
We find the greatest values alpha(1) and alpha(2), and the least values beta(1) and beta(2) such that the inequalities alpha C-1(a,b)+(1-alpha(1))H(a,b) < L(a,b) < beta C-1(a,b)+(1 - beta(1))H(a,b) and alpha C-2(a,b)+(1-alpha(2))H(a,b) < I(a,b) < beta C-2(a,b) + (1 - beta(2))H(a,b) hold for all a, b > 0 with a not equal b. Here, C(a,b),H(a,b), L(a,b), and I(a,b) are the centroidal, harmonic, logarithmic, and identric means of two positive numbers a and b, respectively.
关键词：
For fixed s ≥ 1 and any t 1;t 2 ∈ ( 0;1 / 2 ) we prove that the double inequality G s ( t 1 a + ( 1 - t 1 ) b;t 1 b + ( 1 - t 1 ) a ) A 1 - s ( a;b ) < P ( a;b ) < G s ( t 2 a + ( 1 - t 2 ) b;t 2 b + ( 1 - t 2 ) a ) A 1 - s ( a;b ) holds for all a;b > 0 with a ≠ b if and only if t 1 ≤ ( 1 - 1 - ( 2 / π ) 2 / s ) / 2 and t 2 ≥ ( 1 - 1 / 3 s ) / 2 . Here;P ( a;b );A ( a;b ) and G ( a;b ) denote the Seiffert;arithmetic;and geometric means of two positive numbers a and b;respectively. Published: 2012 First available in Project Euclid: 14 December 2012 zbMATH: 1246.26017 MathSciNet: MR2965473 Digital Object Identifier: 10.1155/2012/684834
摘要：
For fixed s ≥ 1 and any t 1 , t 2 ∈ ( 0,1 / 2 ) we prove that the double inequality G s ( t 1 a + ( 1 - t 1 ) b , t 1 b + ( 1 - t 1 ) a ) A 1 - s ( a , b ) < P ( a , b ) < G s ( t 2 a + ( 1 - t 2 ) b , t 2 b + ( 1 - t 2 ) a ) A 1 - s ( a , b ) holds for all a , b > 0 with a ≠ b if and only if t 1 ≤ ( 1 - 1 - ( 2 / π ) 2 / s ) / 2 and t 2 ≥ ( 1 - 1 / 3 s ) / 2 . Here, P ( a , b ) , A ( a , b ) and G ( a , b ) denote the Seiffert, arithmetic, and geometric means of two positive numbers a and b , respectively.
摘要：
We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.
