期刊：
JOURNAL OF INEQUALITIES AND APPLICATIONS,2014年2014(1):1-11 ISSN：1029-242X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming; Shao, Zhi-Hua] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Qian, Wei-Mao] Huzhou Broadcast & TV Univ, Sch 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：
Neuman means;one-parameter mean;harmonic mean;geometric mean;arithmetic mean;quadratic mean;contraharmonic mean
摘要：
We present the best possible parameters
such that the double inequalities
,
,
,
hold for all
with
, where
,
,
,
are the Neuman means, and
,
,
,
are the one-parameter means. MSC:26E60.
关键词：
Centroidal mean;Harmonic mean;Inequalities;Neuman-Sándor mean
摘要：
In this paper, we answer the question: what are the greatest values alpha(1), alpha(2) and the least values beta(1), beta(2), such that the inequalities alpha T-1(a, b)+(1-alpha(1))H(a, b) < R(a, b) < beta T-1(a, b)+(1-beta(1)) H(a, b) and T-alpha 2 (a, b) H1-alpha 2 (a, b) < R(a, b) < T-beta 2 (a, b) H1-beta 2 (a, b) hold for all a,b > 0 with a not equal b? Here, R(a, b), T(a, b) and H(a, b) denote the Neuman-Sandor, centroidal and harmonic means of two positive numbers a and b, respectively.
期刊：
JOURNAL OF MATHEMATICAL INEQUALITIES,2013年7(2):161-166 ISSN：1846-579X
通讯作者：
Chu, Yu-Ming
作者机构：
[Chu, Yu-Ming] Hunan City Univ, Coll Math & Computat Sci, Yiyang 413000, Peoples R China.;[Wang, Miao-Kun] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China.;[Ma, Xiao-Yan] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China.
通讯机构：
[Chu, Yu-Ming] H;Hunan City Univ, Coll Math & Computat Sci, Yiyang 413000, Peoples R China.
关键词：
Complete elliptic integrals;Contraharmonic mean;Toader mean
摘要：
We find the greatest value lambda and the least value mu in (1/2, 1) such that the double inequality C(lambda a + (1 - lambda)b,lambda b + (1 - lambda)a) < T(a,b) < C(mu a + (1 - mu)b, mu b + (1 - mu)a) holds for all a, b > 0 with a not equal b, and give new bounds for the perimeter of an ellipse. Here, T(a,b) = 2/pi integral(pi/2)(0)root a(2)cos(2)theta + b(2)sin(2)theta d theta, and C(a,b) = (a(2) + b(2))/(a + b) denote the Toader, and contraharmonic means of two positive numbers a and b, respectively.
关键词：
We present the greatest value p such that the inequality P(a;b)>Lp(a;b) holds for all a;b>0 with a≠b;where P(a;b) and Lp(a;b) denote the Seiffert and p th generalized logarithmic means of a and b;respectively. Published: 2013 First available in Project Euclid: 14 March 2014 zbMATH: 1267.26028 MathSciNet: MR3035183 Digital Object Identifier: 10.1155/2013/273653
摘要：
We present the greatest value p such that the inequality P (a, b) > L p (a, b) holds for all a, b > 0 with a ≠ b, where P (a, b) and L p (a, b) denote the Seiffert and p th generalized logarithmic 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; Gong, Wei-Ming] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Shen, Xu-Hui] Huzhou Teachers Coll, Coll Nursing, 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：
First Seiffert mean;Neuman-Sándor mean;Quadratic mean
摘要：
In this paper, we find the least value α and the greatest value β such that the double inequality
holds true for all
with
, where
,
and
are the first Seiffert, Neuman-Sándor and quadratic means of a and b, respectively. MSC:26E60.
摘要：
For a graph G = (V, E), the degree distance of G is defined as DD(G) = Sigma({u,v} subset of V(G)) (d(G)(u) + d(G)(v))d(G)(u,v) where d(G)(u) (or d(u)) is the degree of the vertex u in G, and d(G)(u, v) is the distance between u and v. Let B(n) be the set of bicyclic graph with n vertices. In this paper, we study the degree distance of B(n) by introducing grafting transformations, the lower bounds for DD(G) are determined. The corresponding extremal graphs are characterized as well.
摘要：
We deal with the existence of weak solutions of double degenerate quasilinear parabolic inequalities with a Signorini-Dirichlet-Neumann type mixed boundary condition, which may degenerate in certain subset of the boundary or on a segment in the interior of the domain and in time. The main tools in our study are the maximal monotone property of the derivative operator with zero-initial valued conditions and the theory of pseudomonotone perturbations of maximal monotone mappings.
期刊：
Journal of Applied Mathematics,2013年2013:1-4 ISSN：1110-757X
通讯作者：
Chu, Yu-Ming
作者机构：
[He, Zai-Yin] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China.;[Chu, Yu-Ming; Wang, Miao-Kun] 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：
For a;b>0 with a≠b;the Schwab-Borchardt mean SB(a;b) is defined as SB(a;b)={b2-a2/cos-1(a/b) if ab . In this paper;we find the greatest values of α1 and α2 and the least values of β1 and β2 in [0;1/2] such that H(α1a+(1-α1)b;α1b+(1-α1)a)
摘要：
For a,b > 0 with a not equal b, the Schwab-Borchardtmean SB(a,b) is defined as SB(a,b) = {root b(2)-a(2)/cos(-1) (a/b) if a < b, root a(2) - b(2)/cosh(-1) (a/b) if a > b. In this paper, we find the greatest values of alpha(1) and alpha(2) and the least values of beta(1) and beta(2) in [0, 1/2] such that H(alpha(1)a+(1- alpha(1))b,alpha(1)b+(1-alpha(1))a) < S-AH(a,b) < H(beta(1)a+(1-beta(1))b,beta(1)b+(1-beta(1))a) and H(alpha(2)a+(1-alpha(2))b,alpha(2)b+(1-alpha(2))a) < S-HA(a,b) < H(beta(2)a+ (1-beta(2))b,beta(2)b+(1-beta(2))a). Similarly, we also find the greatest values of alpha(3) and alpha(4) and the least values of beta(3) and beta(4) in [1/2, 1] such that C(alpha(3)a+(1-a(alpha))b,alpha(3)b+(1-alpha(3))a) < S-CA(a,b) < C(beta(3)a+(1-beta(3))b,beta(3)b+(1-beta(3))a) and C(alpha(4)a+(1-alpha(4))b,alpha(4)b+(1-alpha(4))a) < S-AC(a,b) < C(beta(4)a+(1-beta(4))b,beta(4)b+(1-beta(4))a). Here, H(a,b) = 2ab/(a+b),A(a,b) = (a+b)/2, and C(a,b) = (a(2)+b(2))/(a+b) are the harmonic, arithmetic, and contraharmonic means, respectively, and S-HA(a,b) = SB(H,A), S-AH(a,b) = SB(A,H), S-CA(a,b) = SB(C,A), and S-AC(a,b) = SB(A,C) are four Neuman means derived from the Schwab- Borchardt mean.
期刊：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS,2013年43(5):1489-1496 ISSN：0035-7596
通讯作者：
Chu, Y. M.
作者机构：
[Chu, Y. M.; Wang, M. K.] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.;[Qiu, S. L.] Zhejiang Sci Tech Univ, Dept Math, Hangzhou 313018, Zhejiang, Peoples R China.
通讯机构：
[Chu, Y. M.] H;Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China.
摘要：
In this paper, we prove that ${M_p}(K(r),K(r\prime )) \ge K(\sqrt 2 /2)$ and ${M_p}(K(r),K(r\prime )) \le K(\sqrt 2 /2)$ for all r ϵ (0, 1) if and only if $p \ge 1 - 4{[K\sqrt 2 /2]^4}/{\pi ^2} = - 3.789...$ and $q \le (\log 2)/[\log (\pi /2) - \log K(\sqrt 2 /2)] = - 4.180...$, where $K\left( r \right)\, = \,\int_0^{\pi /2} {{{\left( {1 - {r^2}\,{{\sin }^2}\theta } \right)}^{ - 1/2}}d\theta } $ is the complete elliptic integral of the first kind, $r'\, = \,\sqrt {1 - {r^2}} $, and Mp(x, y) is the power mean of order p of two positive numbers x and y.
摘要：
We obtain sharp bounds for the Seiffert mean in terms of a two parameter family of means. Our results generalize and extend the recent bounds presented in the Journal of Inequalities and Applications (2012) and Abstract and Applied Analysis (2012).
摘要：
We find the greatest value alpha(1) and alpha(2), and the least values beta(1) and beta(2), such that the double inequalities alpha C-1(a, b)+(1-alpha(1))A(a, b) < T(a, b) < beta C-1(a, b)+(1-beta(1))A(a, b) and alpha(2)/A(a, b)+(1-alpha(2))/C(a, b) < 1/T(a, b) < beta(2)/A(a, b)+(1-beta(2))/C(a, b) hold for all a, b > 0 with a not equal b. As applications, we get new bounds for the complete elliptic integral of the second kind. Here, C(a, b) = (a(2) + b(2))/(a+b), A(a, b) = (a+b)/2, and T(a, b) = 2/pi integral(pi/2)(0) root a(2)cos(2)theta + b(2)sin(2)theta d theta denote the contraharmonic, arithmetic, and Toader means of two positive numbers a and b, respectively.
期刊：
Ars Combinatoria,2013年111:339-344 ISSN：0381-7032
通讯作者：
Chen, Shubo
作者机构：
[Li, Junfeng; Guo, Hong; Chen, Shubo; Lin, Ren] Hunan City Univ, Coll Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Coll Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
摘要：
The Wiener-Hosoya index was firstly introduced by M. Randić in 2004. For any tree T, the Wiener-Hosoya index is defined as WH(T)= Σ/eEE(T) (h(e) +h[e]) where e = uv is an arbitrary edge of T, and h(e) is the product of the numbers of the vertices in each component of T - e, and h[e] is the product of the numbers of the vertices in each component of T - {u, v}. We shall investigate the Wiener-Hosoya index of trees with diameter not larger than 4, and characterize the extremal graphs in this paper.
摘要：
The authors prove some monotonicity properties of functions involving the generalized Agard distortion function ηK (a, t), and obtain some inequalities for ηK (a, t) and relative distortion functions.
