This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
By transferring the judgment of convex functions of several variables into the judgment of convex... more By transferring the judgment of convex functions of several variables into the judgment of convex functions of one variable, the authors discuss the convexity of some convex functions of several variables.
In this paper, we apply Karamata's theorem combined with majorization theory to establish a new i... more In this paper, we apply Karamata's theorem combined with majorization theory to establish a new inequality for the upper bound of the product of two …nite sums of convex functions. As applications, we derive some new generalizations of Kantorovich's inequality.
By the properties of a Schur-convex function, Schur-convexity of the dual form of some symmetric ... more By the properties of a Schur-convex function, Schur-convexity of the dual form of some symmetric functions is simply proved.
The Schur convexity and Schur-geometric convexity of generalized Heronian means involving two par... more The Schur convexity and Schur-geometric convexity of generalized Heronian means involving two parameters are studied, the main result is then used to obtain several interesting and significantly inequalities for generalized Heronian means.
By the properties of Schur-convex function, Schur geometrically convex function and Schur harmoni... more By the properties of Schur-convex function, Schur geometrically convex function and Schur harmonically convex function, Schur-convexity, Schur geometric and Schur harmonic convexities of the dual form for a class of symmetric functions are simply proved. As an application, several inequalities are obtained, some of which extend the known ones.
In the paper, the authors find Schur-harmonic convexity of linear combinations of differences bet... more In the paper, the authors find Schur-harmonic convexity of linear combinations of differences between some means such as the arithmetic, geometric, harmonic, and root-square means, and establish some inequalities related to these means and differences.
In this paper, by applying the decision theorem of the Schur-power convex function, the Schur-pow... more 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 studied. As applications, some new inequalities are established.
The judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric... more The judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric functions are given. As their application, some analytic inequalities are established.
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright
By using methods in the theory of majorization, a double inequality for the gamma function is ext... more By using methods in the theory of majorization, a double inequality for the gamma function is extended to the k-gamma function and the k-Riemann zeta function.
The Schur-convexity, the Schur-geometric convexity and the Schurharmonic convexity of two mapping... more The Schur-convexity, the Schur-geometric convexity and the Schurharmonic convexity of two mappings which related to Hadamard-type integral inequalities are researched. And three refinements of Hadamard-type integral inequality are obtained, as applications, some inequalities related to the arithmetic mean, the logarithmic mean and the power mean are established.
The Schur-convexity for certain compound functions involving the dual of the complete symmetric f... more The Schur-convexity for certain compound functions involving the dual of the complete symmetric function is studied. As an application, the Schur-convexity of some special symmetric functions is discussed and some inequalities are established.
Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a mean of two variabl... more Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a mean of two variables with three parameters are investigated, and some mean value inequalities of two variables are established.
This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY
By transferring the judgment of convex functions of several variables into the judgment of convex... more By transferring the judgment of convex functions of several variables into the judgment of convex functions of one variable, the authors discuss the convexity of some convex functions of several variables.
In this paper, we apply Karamata's theorem combined with majorization theory to establish a new i... more In this paper, we apply Karamata's theorem combined with majorization theory to establish a new inequality for the upper bound of the product of two …nite sums of convex functions. As applications, we derive some new generalizations of Kantorovich's inequality.
By the properties of a Schur-convex function, Schur-convexity of the dual form of some symmetric ... more By the properties of a Schur-convex function, Schur-convexity of the dual form of some symmetric functions is simply proved.
The Schur convexity and Schur-geometric convexity of generalized Heronian means involving two par... more The Schur convexity and Schur-geometric convexity of generalized Heronian means involving two parameters are studied, the main result is then used to obtain several interesting and significantly inequalities for generalized Heronian means.
By the properties of Schur-convex function, Schur geometrically convex function and Schur harmoni... more By the properties of Schur-convex function, Schur geometrically convex function and Schur harmonically convex function, Schur-convexity, Schur geometric and Schur harmonic convexities of the dual form for a class of symmetric functions are simply proved. As an application, several inequalities are obtained, some of which extend the known ones.
In the paper, the authors find Schur-harmonic convexity of linear combinations of differences bet... more In the paper, the authors find Schur-harmonic convexity of linear combinations of differences between some means such as the arithmetic, geometric, harmonic, and root-square means, and establish some inequalities related to these means and differences.
In this paper, by applying the decision theorem of the Schur-power convex function, the Schur-pow... more 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 studied. As applications, some new inequalities are established.
The judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric... more The judgement theorems of Schur geometric and Schur harmonic convexities for a class of symmetric functions are given. As their application, some analytic inequalities are established.
This article appeared in a journal published by Elsevier. The attached copy is furnished to the a... more This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright
By using methods in the theory of majorization, a double inequality for the gamma function is ext... more By using methods in the theory of majorization, a double inequality for the gamma function is extended to the k-gamma function and the k-Riemann zeta function.
The Schur-convexity, the Schur-geometric convexity and the Schurharmonic convexity of two mapping... more The Schur-convexity, the Schur-geometric convexity and the Schurharmonic convexity of two mappings which related to Hadamard-type integral inequalities are researched. And three refinements of Hadamard-type integral inequality are obtained, as applications, some inequalities related to the arithmetic mean, the logarithmic mean and the power mean are established.
The Schur-convexity for certain compound functions involving the dual of the complete symmetric f... more The Schur-convexity for certain compound functions involving the dual of the complete symmetric function is studied. As an application, the Schur-convexity of some special symmetric functions is discussed and some inequalities are established.
Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a mean of two variabl... more Schur-convexity, Schur-geometric convexity and Schur-harmonic convexity for a mean of two variables with three parameters are investigated, and some mean value inequalities of two variables are established.
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