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Journal of Inequalities and Applications, ISSN 1025-5834, 12/2013, Volume 2013, Issue 1, pp. 1 - 9
The judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric functions are given. As their application, some analytic... 
Schur geometric convexity | inequality | Analysis | Schur harmonic convexity | symmetric function | Mathematics, general | Mathematics | Applications of Mathematics | Symmetric function | Inequality | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
SpringerPlus, ISSN 2193-1801, 12/2016, Volume 5, Issue 1, pp. 1 - 8
In this paper, using the properties of Schur-convex function, Schur-geometrically convex function and Schur-harmonically convex function, we provide much... 
Schur-convexity | Schur-harmonic convexity | Complete symmetric function | Schur-geometric convexity | Science | Primary 05E05 | 26B25 | Science, general | MULTIDISCIPLINARY SCIENCES
Journal Article
Advances in the theory of nonlinear analysis and its applications, ISSN 2587-2648, 06/2019, Volume 3, Issue 2, pp. 74 - 89
By using the decision theorem and properties of the Schur-convex function, the Schur-geometric convex function and the Schur-harmonic function, the Schur-... 
schur-convexity; schur-geometric convexity; schur-harmonic convexity; completely symmetric function; dual form
Journal Article
by Shi, HN and Wang, P and Zhang, J
JOURNAL OF INEQUALITIES AND APPLICATIONS, ISSN 1029-242X, 03/2020, Volume 2020, Issue 1, pp. 1 - 11
The Schur-convexity for certain compound functions involving the dual of the complete symmetric function is studied. As an application, the Schur-convexity of... 
MATHEMATICS | Schur-convexity | MATHEMATICS, APPLIED | Schur-harmonic convexity | INEQUALITIES | CONCAVITY | Schur-geometric convexity | FORM | Dual form | Completely symmetric function | HARMONIC CONVEXITIES | Convexity
Journal Article
Advanced Studies in Contemporary Mathematics (Kyungshang), ISSN 1229-3067, 2017, Volume 27, Issue 4, pp. 599 - 608
Journal Article
Symmetry (Basel), ISSN 2073-8994, 2019, Volume 11, Issue 7, p. 897
In this paper, by applying the decision theorem of the Schur-power convex function, the Schur-power convexity of a class of complete symmetric functions are... 
Schur-convexity | Schur-harmonic convexity | Schur-power convexity | Schur-geometric convexity | FORM | MULTIDISCIPLINARY SCIENCES | dual form | completely symmetric function | HARMONIC CONVEXITIES
Journal Article
Advanced Studies in Contemporary Mathematics (Kyungshang), ISSN 1229-3067, 10/2016, Volume 26, Issue 4, pp. 681 - 684
Journal Article
Journal of Number Theory, ISSN 0022-314X, 09/2017, Volume 178, pp. 47 - 59
The main aim of the article is to prove that the symmetric function Φn(x,r)=∏i1+i2+⋯+in=r(x1i1+x2i2+⋯+xnin) is Schur geometrically convex for x∈R++n and fixed... 
Schur geometric convexity | Schur m-power convex | Symmetric function | Arithmetic–geometric inequality | Schur harmonic convexity | Inequality | MATHEMATICS | Arithmetic-geometric inequality | SCHUR POWER CONVEXITY | EXTENDED MEAN-VALUES
Journal Article
Filomat, ISSN 0354-5180, 2018, Volume 32, Issue 19, pp. 6643 - 6651
Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a mean of two variables with three parameters are investigated, and some mean value... 
Schur-convexity | Schur-harmonic convexity | Schur-geometric convexity | Inequalities | Majorization | Mean of two variables | MATHEMATICS, APPLIED | inequalities | CONCAVITY | SUFFICIENT CONDITIONS | HARMONIC-CONVEXITY | mean of two variables | POWER CONVEXITY | MATHEMATICS | VALUES | majorization
Journal Article
Proceedings of the Jangjeon Mathematical Society, ISSN 1598-7264, 2014, Volume 17, Issue 3, pp. 383 - 392
Journal Article
Journal of Nonlinear Science and Applications, ISSN 2008-1898, 2016, Volume 9, Issue 5, pp. 2298 - 2304
The Schur-m power convexity of a mean for two variables with three parameters is investigated and a judging condition about the Schur-m power convexity of a... 
Schur geometric convexity | Schur-m power convexity | Majorization | Schur harmonic convexity | Mean of two variables | Schur convexity | MATHEMATICS | majorization | STOLARSKY
Journal Article
Journal of Nonlinear Science and Applications, ISSN 2008-1898, 2016, Volume 9, Issue 10, pp. 5510 - 5520
Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for Lehmer mean of n variables are investigated, and some mean value inequalities of n... 
Schur geometric convexity | Inequalities | Majorization | N variables lehmer mean | Schur harmonic convexity | Schur convexity | POWER CONVEXITY | MATHEMATICS | inequalities | HOLDER | n variables Lehmer mean | VALUES | majorization | HARMONIC-CONVEXITY | STOLARSKY
Journal Article
Journal of Mathematical Inequalities, ISSN 1846-579X, 2014, Volume 8, Issue 2, pp. 349 - 358
By the properties of Schur-convex function, Schur geometrically convex function and Schur harmonically convex function, Schur-convexity, Schur geometric and... 
Schur geometric convexity | Schur-convexity | Log-convex function | Symmetric functions | Schur harmonic convexity | Dual form | Inequality | MATHEMATICS | inequality | MATHEMATICS, APPLIED | symmetric functions | CONCAVITY | dual form | GINI MEAN-VALUES | log-convex function
Journal Article
Mathematical Inequalities and Applications, ISSN 1331-4343, 2013, Volume 16, Issue 4, pp. 963 - 970
In this paper, the Schur-convexity, the Schur-geometric-convexity and the Schur-harmonic-convexity of dual form of the complete symmetric function are... 
Schur- geometricconvexity | Schur-convexity | Dual form | Complete symmetric function | Schur-harmonic-convexity | MATHEMATICS | Schur-geometric-convexity | CONCAVITY | SUFFICIENT CONDITIONS | complete symmetric function | dual form | MEAN-VALUES | HARMONIC-CONVEXITY
Journal Article
Mathematical Inequalities and Applications, ISSN 1331-4343, 2007, Volume 10, Issue 4, pp. 745 - 753
A new. symmetric function, which generalizes Hamy symmetric function, is defined. Its properties, including Schur-geometric convexity, are investigated. Some... 
Hamy symmetric function | Schur-geometric convexity | Multiplicatively convex function | MATHEMATICS | INEQUALITIES | multiplicatively convex function
Journal Article
Taiwanese journal of mathematics, ISSN 1027-5487, 12/2011, Volume 15, Issue 6, pp. 2721 - 2731
In this paper, we give the sufficient as well as necessary condition of the Schur-convexity and Schur-harmonic-convexity of the generalized Heronian means with... 
Generalized heronian means | Arithmetic-geometric-harmonic means inequalities | Heronian means | Schur-convexity | Schur-geometric-convexity | Schurharmonic-convexity | MATHEMATICS | Schur-harmonic-convexity | Generalized Heronian means | VALUES
Journal Article
Mathematical Inequalities and Applications, ISSN 1331-4343, 2011, Volume 14, Issue 4, pp. 897 - 903
Journal Article
MATHEMATICAL INEQUALITIES & APPLICATIONS, ISSN 1331-4343, 10/2011, Volume 14, Issue 4, pp. 897 - 903
We prove that the four-parameter family of means R(u, v; r, s; x, y) = [E(r, s; x(u), y(u)]/E(r, s; x(v), y(v))](1/(u-v)) is Schur-geometrically convex... 
MATHEMATICS | Schur-convexity | Schur-geometric convexity | GINI MEANS | S-means | Stolarsky mean | Gini mean | EXTENDED MEAN-VALUES
Journal Article
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