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Notes on judgment criteria of convex functions of several variables

Cilt: 4 Sayı: 4 31 Aralık 2021
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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

Kaynakça

  1. [1] X.-D. Chen, Remarks on convex functions, Journal of Western Chongqing University Natural Science Edition 2 (2003), no. 2, 37-40; available online at http://dx.chinadoi.cn/10.3969/j.issn.1673-8012.2003.04.012. (Chinese)
  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.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

31 Aralık 2021

Gönderilme Tarihi

24 Ağustos 2021

Kabul Tarihi

29 Eylül 2021

Yayımlandığı Sayı

Yıl 2021 Cilt: 4 Sayı: 4

Kaynak Göster

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, ve 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 (01 Aralık 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, ve W.- shih Du, “Notes on judgment criteria of convex functions of several variables”, RNA, c. 4, sy 4, ss. 235–243, Ara. 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 (01 Aralık 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, vd. “Notes on judgment criteria of convex functions of several variables”. Results in Nonlinear Analysis, c. 4, sy 4, Aralık 2021, ss. 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. 01 Aralık 2021;4(4):235-43. doi:10.53006/rna.986088

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