Research Article

Notes on judgment criteria of convex functions of several variables

Volume: 4 Number: 4 December 31, 2021
EN

Notes on judgment criteria of convex functions of several variables

Abstract

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.

Keywords

References

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  2. [2] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite?Hadamard Inequalities and Applications, Amended version, RGMIA Monographs, Victoria University, 2002; available online at http://rgmia.org/monographs/hermite_hadamard. html.
  3. [3] N. Elezovi¢ and J. Pecaric, A note on Schur-convex functions, Rocky Mountain J. Math. 30 (2000), no. 3, 853?856; available online at https://doi.org/10.1216/rmjm/1021477248.
  4. [4] A.W. Marshall, I. Olkin, and B.C. Arnold, Inequalities: Theory of Majorization and its Applications, 2nd Ed., Springer Ver- lag, New York-Dordrecht-Heidelberg-London, 2011; available online at http://dx.doi.org/10.1007/978-0-387-68276-1.
  5. [5] F. Qi, Inequalities for an integral, Math. Gaz. 80 (1996), no. 488, 376-377; available online at https://doi.org/10.2307/ 3619581.
  6. [6] F. Qi, Pólya type integral inequalities: origin, variants, proofs, refinements, generalizations, equivalences, and applications, Math. Inequal. Appl. 18 (2015), no. 1, 1-38; available online at https://doi.org/10.7153/mia-18-01.
  7. [7] F. Qi, J. Sándor, S.S. Dragomir, and A. Sofo, Notes on the Schur-convexity of the extended mean values, Taiwanese J. Math. 9 (2005), no. 3, 411-420; available online at https://doi.org/10.11650/twjm/1500407849.
  8. [8] H.-N. Shi, S.-H. Wu, and F. Qi, An alternative note on the Schur-convexity of the extended mean values, Math. Inequal. Appl. 9 (2006), no. 2, 219-224; available online at http://dx.doi.org/10.7153/mia-09-22.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Pei Wang This is me
China

Jian Zhang This is me
China

Publication Date

December 31, 2021

Submission Date

August 24, 2021

Acceptance Date

September 29, 2021

Published in Issue

Year 2021 Volume: 4 Number: 4

APA
Shi, H., Wang, P., Zhang, J., & Du, W.- shih. (2021). Notes on judgment criteria of convex functions of several variables. Results in Nonlinear Analysis, 4(4), 235-243. https://doi.org/10.53006/rna.986088
AMA
1.Shi H, Wang P, Zhang J, Du W shih. Notes on judgment criteria of convex functions of several variables. RNA. 2021;4(4):235-243. doi:10.53006/rna.986088
Chicago
Shi, Huannan, Pei Wang, Jian Zhang, and Wei-shih Du. 2021. “Notes on Judgment Criteria of Convex Functions of Several Variables”. Results in Nonlinear Analysis 4 (4): 235-43. https://doi.org/10.53006/rna.986088.
EndNote
Shi H, Wang P, Zhang J, Du W- shih (December 1, 2021) Notes on judgment criteria of convex functions of several variables. Results in Nonlinear Analysis 4 4 235–243.
IEEE
[1]H. Shi, P. Wang, J. Zhang, and W.- shih Du, “Notes on judgment criteria of convex functions of several variables”, RNA, vol. 4, no. 4, pp. 235–243, Dec. 2021, doi: 10.53006/rna.986088.
ISNAD
Shi, Huannan - Wang, Pei - Zhang, Jian - Du, Wei-shih. “Notes on Judgment Criteria of Convex Functions of Several Variables”. Results in Nonlinear Analysis 4/4 (December 1, 2021): 235-243. https://doi.org/10.53006/rna.986088.
JAMA
1.Shi H, Wang P, Zhang J, Du W- shih. Notes on judgment criteria of convex functions of several variables. RNA. 2021;4:235–243.
MLA
Shi, Huannan, et al. “Notes on Judgment Criteria of Convex Functions of Several Variables”. Results in Nonlinear Analysis, vol. 4, no. 4, Dec. 2021, pp. 235-43, doi:10.53006/rna.986088.
Vancouver
1.Huannan Shi, Pei Wang, Jian Zhang, Wei-shih Du. Notes on judgment criteria of convex functions of several variables. RNA. 2021 Dec. 1;4(4):235-43. doi:10.53006/rna.986088

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