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Journal of inequalities and applications, ISSN 1029-242X, 2019, Volume 2019, Issue 1, pp. 1 - 13
In the article, we present several majorization theorems for strongly convex functions and give their applications in inequality theory. The given results are... 
39B62 | Majorization theorem | 26A51 | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Convexity | 26D15 | Strongly convex function | MATHEMATICS, APPLIED | SERIES | CONCAVITY | SCHUR HARMONIC CONVEXITY | POWER MEAN INEQUALITY | HYPERGEOMETRIC-FUNCTIONS | MATHEMATICS | COMPLETE ELLIPTIC INTEGRALS | REFINEMENTS | RESPECT | BOUNDS | TRANSFORMATION INEQUALITIES | Theorems | Convex analysis
Journal Article
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
Analysis (Wiesbaden), ISSN 0174-4747, 2012, Volume 32, Issue 4, pp. 263 - 270
In the paper, the authors discuss the Schur-harmonic convexity on (0,∞) × (0,∞) for differences of some famous means, such as the arithmetic, geometric,... 
inequality | difference | Schur-harmonic convexity | majorization | mean
Journal Article
Indian journal of pure and applied mathematics, ISSN 0975-7465, 2012, Volume 43, Issue 3, pp. 227 - 249
For x = (x 1, x 2, ..., x n ) ∈ ℝ + n , the symmetric function ψ n (x, r) is defined by $$\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) =... 
Schur convex | Numerical Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Symmetric function | Schur multiplicatively convex | Schur harmonic convex | MATHEMATICS | DUAL FORM | RESPECT | INEQUALITIES | CONCAVITY | SCHUR-HARMONIC-CONVEXITY
Journal Article
Journal of function spaces, ISSN 2314-8888, 2019, Volume 2019, pp. 1 - 8
In the article, we present several conformable fractional integrals’ versions of the Hermite-Hadamard type inequalities for GG- and GA-convex functions and... 
FRACTIONAL INTEGRALS | MATHEMATICS | MATHEMATICS, APPLIED | SCHUR HARMONIC CONVEXITY | CONCAVITY | Bivariate analysis | Mathematical functions | Applied mathematics | Integrals | Convex analysis | Inequalities
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
Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 13
In this paper, we investigate Schur-harmonic convexity of some functions which are obtained from the co-ordinated harmonically convex functions on a square in... 
Schur-convexity | 26A51 | Schur-harmonic convexity | Analysis | Convex functions on the co-ordinates | Harmonically convex | Mathematics, general | Mathematics | Applications of Mathematics | 26D15 | MATHEMATICS | MATHEMATICS, APPLIED | Harmonic functions | Convex analysis | Convexity
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
Mathematische Nachrichten, ISSN 0025-584X, 2011, Volume 284, Issue 5-6, pp. 653 - 663
This paper investigates the Schur multiplicative and harmonic convexities of the complete symmetric function... 
Schur multiplicative convexity | MSC 26B25 | Complete symmetric function | theory of majorization | Schur harmonic convexity | MATHEMATICS | INEQUALITIES | FAMILIES | EXTENDED MEAN-VALUES
Journal Article
Journal of Mathematical Inequalities, ISSN 1846-579X, 2014, Volume 8, Issue 2, pp. 321 - 330
In the paper, the authors find Schur-harmonic convexity of linear combinations of differences between some means such as the arithmetic, geometric, harmonic,... 
Mean | Schur-harmonic convexity | Difference | MATHEMATICS | MATHEMATICS, APPLIED | difference | mean
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
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