Araştırma Makalesi
BibTex RIS Kaynak Göster

Notes on judgment criteria of convex functions of several variables

Yıl 2021, , 235 - 243, 31.12.2021
https://doi.org/10.53006/rna.986088

Öz

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.

Kaynakça

  • [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] 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] 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] 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] F. Qi, Inequalities for an integral, Math. Gaz. 80 (1996), no. 488, 376-377; available online at https://doi.org/10.2307/ 3619581.
  • [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] 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] 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.
  • [9] Y. Shuang and F. Qi, Integral inequalities of Hermite-Hadamard type for extended s-convex functions and applications, Mathematics 6 (2018), no. 11, Article 223, 12 pages; available online at https://doi.org/10.3390/math6110223.
  • [10] B.-Y. Wang, Foundations of Majorization Inequalities, Beijing Normal University Press, Beijing, 1990. (Chinese)
  • [11] S.-G. Wang, M.-X. Wu, and Z.-Z. Jia, Inequalities in Matrix Theory, Second Ed., Science Press, Beijing, 2006.
  • [12] J.-J. Wu and Y.-G. Zhu, Several methods for determining the convexity of a function, Journal of Communication University of China Science and Technology, 27 (2002), no. 6, 79-83. (Chinese)
  • [13] D.E. Wulbert, Favard's inequality on average values of convex functions, Math. Comput. Modelling 37 (2003), no. 12-13, 1383?1391; available online at https://doi.org/10.1016/S0895-7177(03)90048-3.
  • [14] X.M. Zhang and Y.M. Chu, Convexity of the integral arithmetic mean of a convex function, Rocky Mountain J. Math. 40 (2010), no. 3, 1061-1068; available online at https://doi.org/10.1216/RMJ-2010-40-3-1061.
  • [15] N. G. Zheng, X.M. Zhang, and Y.M. Chu, Convexity and geometrical convexity of exponential and logarithmic means in N variables, Acta Math. Sci. Ser. A (Chin. Ed.) 28 (2008), no. 6, 1173?1180. (Chinese)
Yıl 2021, , 235 - 243, 31.12.2021
https://doi.org/10.53006/rna.986088

Öz

Kaynakça

  • [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] 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] 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] 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] F. Qi, Inequalities for an integral, Math. Gaz. 80 (1996), no. 488, 376-377; available online at https://doi.org/10.2307/ 3619581.
  • [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] 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] 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.
  • [9] Y. Shuang and F. Qi, Integral inequalities of Hermite-Hadamard type for extended s-convex functions and applications, Mathematics 6 (2018), no. 11, Article 223, 12 pages; available online at https://doi.org/10.3390/math6110223.
  • [10] B.-Y. Wang, Foundations of Majorization Inequalities, Beijing Normal University Press, Beijing, 1990. (Chinese)
  • [11] S.-G. Wang, M.-X. Wu, and Z.-Z. Jia, Inequalities in Matrix Theory, Second Ed., Science Press, Beijing, 2006.
  • [12] J.-J. Wu and Y.-G. Zhu, Several methods for determining the convexity of a function, Journal of Communication University of China Science and Technology, 27 (2002), no. 6, 79-83. (Chinese)
  • [13] D.E. Wulbert, Favard's inequality on average values of convex functions, Math. Comput. Modelling 37 (2003), no. 12-13, 1383?1391; available online at https://doi.org/10.1016/S0895-7177(03)90048-3.
  • [14] X.M. Zhang and Y.M. Chu, Convexity of the integral arithmetic mean of a convex function, Rocky Mountain J. Math. 40 (2010), no. 3, 1061-1068; available online at https://doi.org/10.1216/RMJ-2010-40-3-1061.
  • [15] N. G. Zheng, X.M. Zhang, and Y.M. Chu, Convexity and geometrical convexity of exponential and logarithmic means in N variables, Acta Math. Sci. Ser. A (Chin. Ed.) 28 (2008), no. 6, 1173?1180. (Chinese)
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Huannan Shi

Pei Wang Bu kişi benim

Jian Zhang Bu kişi benim

Wei-shih Du 0000-0001-8996-2270

Yayımlanma Tarihi 31 Aralık 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Shi, H., Wang, P., Zhang, J., Du, W.-s. (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 Shi H, Wang P, Zhang J, Du Ws. Notes on judgment criteria of convex functions of several variables. RNA. Aralık 2021;4(4):235-243. doi:10.53006/rna.986088
Chicago Shi, Huannan, Pei Wang, Jian Zhang, ve Wei-shih Du. “Notes on Judgment Criteria of Convex Functions of Several Variables”. Results in Nonlinear Analysis 4, sy. 4 (Aralık 2021): 235-43. https://doi.org/10.53006/rna.986088.
EndNote Shi H, Wang P, Zhang J, Du W-s (01 Aralık 2021) Notes on judgment criteria of convex functions of several variables. Results in Nonlinear Analysis 4 4 235–243.
IEEE H. Shi, P. Wang, J. Zhang, ve W.-s. Du, “Notes on judgment criteria of convex functions of several variables”, RNA, c. 4, sy. 4, ss. 235–243, 2021, doi: 10.53006/rna.986088.
ISNAD Shi, Huannan vd. “Notes on Judgment Criteria of Convex Functions of Several Variables”. Results in Nonlinear Analysis 4/4 (Aralık 2021), 235-243. https://doi.org/10.53006/rna.986088.
JAMA Shi H, Wang P, Zhang J, Du W-s. 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, 2021, ss. 235-43, doi:10.53006/rna.986088.
Vancouver Shi H, Wang P, Zhang J, Du W-s. Notes on judgment criteria of convex functions of several variables. RNA. 2021;4(4):235-43.