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Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$

Yıl 2024, Cilt: 53 Sayı: 2, 417 - 432, 23.04.2024

Yi Cao Jianmiao Ruan

https://doi.org/10.15672/hujms.1283922

Öz

In this paper, the concept of the $(p,h)$-convex function is introduced, which generalizes the $p$-convex function and the $h$-convex function, and Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$ are established. Furthermore, some mappings related to the above inequalities are studied and some known results are generalized.

Anahtar Kelimeler

the $p$-convex set the $(p,h)$-convex function, Hermite-Hadamard type inequalities mapping

Kaynakça

  • [1] M. Alomari and M. Darus, Hadamard-type inequalities for s-convex functions, Int. Math. Forum 3 (40), 1965-1975, 2008.
  • [2] M. Alomari and M. Darus, The Hermite-Hadamard’ s inequality for s-convex function of 2-variables on the co-ordinates, Int. J. Math. Anal. 2 (13), 629-638, 2008.
  • [3] W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter Konvexer funktionen in topologischen linearen Raumen, Publ. Inst. Math. 23, 13-20, 1978.
  • [4] P. Burai and A. Házy, On approximately h-convex functions, J. Convex Anal. 18 (2), 1-9, 2011.
  • [5] S. Dragomir, Two mappings in connection to Hadamard’s inequality, J. Math. Anal. Appl. 167, 49-56, 1992.
  • [6] S. Dragomir, On the Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J. Math. 5 (4), 775-788, 2001.
  • [7] S. Dragomir and S. Fitzpatrick, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math. 32 (4), 687-696, 1999.
  • [8] S. Dragomir and C. Pearce, Selected topics on Hermite-Hadamard inequalities and Applications, RGMIA Monographs, Victoria University, 2000. (ONLINE: http://rgmia.vu.edu.au/monographs/).
  • [9] S. Dragomir, J. Pe˘caric and L. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21, 335-241, 1995.
  • [10] Z. Eken, S. Kemali, G. Tnaztepe and G. Adilov, The Hermite-Hadamard inequalities for p-convex functions, Hacet. J. Math. Stat. 20 (5), 1242-1253, 2021.
  • [11] M. Feng, J. Ruan and X. Ma, Hermite-Hadamard type inequalities for multidimensional strongly h-convex functions, Math. Inequal. Appl. 24 (4), 897-911, 2021.
  • [12] E. Godunova and V. Levin, Neravenstva dlja funkcii sirokogo klassa soderzascego vypuklye monotonnye i nekotorye drugie vidy funkii, Vycislitel, Mat. i. Fiz. Mezvuzov. Sb. Nauc. MGPI Moskva 9, 138-142, 1985.
  • [13] A. Házy, Bernstein-Doetsch type results for h-convex functions, Math. Inequal. Appl. 14 (3), 499-508, 2011.
  • [14] W. Hong, Y. Xu, J. Ruan and X. Ma, Some new estimates for srongly h-convex functions on co-ordiantes, 2021, https://www.researchgate.net/publication/357484089.
  • [15] X. Jin, B. Jin, J. Ruan and X. Ma, Some characterizations of h-convex functions, J. Math. Inequal. 16 (2), 751-764, 2022.
  • [16] J. Kim, V. Yaskin and A. Zvavitch, The geometry of p-convex intersection bodies, Adv. Math. 226, 5321-5337, 2011.
  • [17] M. Latif and M. Alomari, On Hadamard-type inequalities for h-convex functions on the co-ordinates, Int. J. Math. Anal. 3 (33), 1645-1656, 2009.
  • [18] M. Matłoka, On some Hadamard-type inequalities for $(h_{1}, h_{2})$-preinvex functions on the co-ordinates, J. Inequal. Appl. 2013, 227, 2013.
  • [19] M. Matłoka, On Hadamard’s inequality for h-convex function on a disk, Appl. Math. Comput. 235, 118-123, 2014.
  • [20] A. Olbrys, Representation theorems for h-convexity, J. Math. Anal. Appl. 426, 986- 994, 2015.
  • [21] C. Pearce and A. Rubinov, P-functions, quasi-convex functions and Hadamard-type inequalities, J. Math. Anal. Appl. 240, 92-104, 1999.
  • [22] M. Z. Sarikaya, A. Saglam and H. Yildirim, On some Hadamard-Type inequalities for h-convex functions, J. Math. Inequal. 2(3), 335-341, 2008.
  • [23] S. Sezer, Z. Eken, G. Tnaztepe and G. Adilov, p-convex functions and some of their properties, Numer. Funct. Anal. Optim. 42 (4), 443-459, 2021.
  • [24] S. Varo˘sanec, On h-convexity, J. Math. Anal. Appl. 326, 303-311, 2007.
  • [25] X. Wang, J. Ruan and X. Ma, On the Hermite-Hadamard inequalities for h-convex functions on balls and ellipsoids, Filomat, 33 (18), 5817-5886, 2019.

Yıl 2024, Cilt: 53 Sayı: 2, 417 - 432, 23.04.2024

Yi Cao Jianmiao Ruan

https://doi.org/10.15672/hujms.1283922

Öz

Kaynakça

  • [1] M. Alomari and M. Darus, Hadamard-type inequalities for s-convex functions, Int. Math. Forum 3 (40), 1965-1975, 2008.
  • [2] M. Alomari and M. Darus, The Hermite-Hadamard’ s inequality for s-convex function of 2-variables on the co-ordinates, Int. J. Math. Anal. 2 (13), 629-638, 2008.
  • [3] W. Breckner, Stetigkeitsaussagen für eine Klasse verallgemeinerter Konvexer funktionen in topologischen linearen Raumen, Publ. Inst. Math. 23, 13-20, 1978.
  • [4] P. Burai and A. Házy, On approximately h-convex functions, J. Convex Anal. 18 (2), 1-9, 2011.
  • [5] S. Dragomir, Two mappings in connection to Hadamard’s inequality, J. Math. Anal. Appl. 167, 49-56, 1992.
  • [6] S. Dragomir, On the Hadamard’s inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J. Math. 5 (4), 775-788, 2001.
  • [7] S. Dragomir and S. Fitzpatrick, The Hadamard’s inequality for s-convex functions in the second sense, Demonstratio Math. 32 (4), 687-696, 1999.
  • [8] S. Dragomir and C. Pearce, Selected topics on Hermite-Hadamard inequalities and Applications, RGMIA Monographs, Victoria University, 2000. (ONLINE: http://rgmia.vu.edu.au/monographs/).
  • [9] S. Dragomir, J. Pe˘caric and L. Persson, Some inequalities of Hadamard type, Soochow J. Math. 21, 335-241, 1995.
  • [10] Z. Eken, S. Kemali, G. Tnaztepe and G. Adilov, The Hermite-Hadamard inequalities for p-convex functions, Hacet. J. Math. Stat. 20 (5), 1242-1253, 2021.
  • [11] M. Feng, J. Ruan and X. Ma, Hermite-Hadamard type inequalities for multidimensional strongly h-convex functions, Math. Inequal. Appl. 24 (4), 897-911, 2021.
  • [12] E. Godunova and V. Levin, Neravenstva dlja funkcii sirokogo klassa soderzascego vypuklye monotonnye i nekotorye drugie vidy funkii, Vycislitel, Mat. i. Fiz. Mezvuzov. Sb. Nauc. MGPI Moskva 9, 138-142, 1985.
  • [13] A. Házy, Bernstein-Doetsch type results for h-convex functions, Math. Inequal. Appl. 14 (3), 499-508, 2011.
  • [14] W. Hong, Y. Xu, J. Ruan and X. Ma, Some new estimates for srongly h-convex functions on co-ordiantes, 2021, https://www.researchgate.net/publication/357484089.
  • [15] X. Jin, B. Jin, J. Ruan and X. Ma, Some characterizations of h-convex functions, J. Math. Inequal. 16 (2), 751-764, 2022.
  • [16] J. Kim, V. Yaskin and A. Zvavitch, The geometry of p-convex intersection bodies, Adv. Math. 226, 5321-5337, 2011.
  • [17] M. Latif and M. Alomari, On Hadamard-type inequalities for h-convex functions on the co-ordinates, Int. J. Math. Anal. 3 (33), 1645-1656, 2009.
  • [18] M. Matłoka, On some Hadamard-type inequalities for $(h_{1}, h_{2})$-preinvex functions on the co-ordinates, J. Inequal. Appl. 2013, 227, 2013.
  • [19] M. Matłoka, On Hadamard’s inequality for h-convex function on a disk, Appl. Math. Comput. 235, 118-123, 2014.
  • [20] A. Olbrys, Representation theorems for h-convexity, J. Math. Anal. Appl. 426, 986- 994, 2015.
  • [21] C. Pearce and A. Rubinov, P-functions, quasi-convex functions and Hadamard-type inequalities, J. Math. Anal. Appl. 240, 92-104, 1999.
  • [22] M. Z. Sarikaya, A. Saglam and H. Yildirim, On some Hadamard-Type inequalities for h-convex functions, J. Math. Inequal. 2(3), 335-341, 2008.
  • [23] S. Sezer, Z. Eken, G. Tnaztepe and G. Adilov, p-convex functions and some of their properties, Numer. Funct. Anal. Optim. 42 (4), 443-459, 2021.
  • [24] S. Varo˘sanec, On h-convexity, J. Math. Anal. Appl. 326, 303-311, 2007.
  • [25] X. Wang, J. Ruan and X. Ma, On the Hermite-Hadamard inequalities for h-convex functions on balls and ellipsoids, Filomat, 33 (18), 5817-5886, 2019.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Yi Cao Bu kişi benim 0009-0003-7632-0713

Jianmiao Ruan 0000-0003-0916-6763

Erken Görünüm Tarihi 15 Ağustos 2023
Yayımlanma Tarihi 23 Nisan 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 53 Sayı: 2

Kaynak Göster

APA Cao, Y., & Ruan, J. (2024). Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$. Hacettepe Journal of Mathematics and Statistics, 53(2), 417-432. https://doi.org/10.15672/hujms.1283922
AMA Cao Y, Ruan J. Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$. Hacettepe Journal of Mathematics and Statistics. Nisan 2024;53(2):417-432. doi:10.15672/hujms.1283922
Chicago Cao, Yi, ve Jianmiao Ruan. “Hermite-Hadamard Type Inequalities for $(p,h)$-Convex Functions on $\mathbb{R}^n$”. Hacettepe Journal of Mathematics and Statistics 53, sy. 2 (Nisan 2024): 417-32. https://doi.org/10.15672/hujms.1283922.
EndNote Cao Y, Ruan J (01 Nisan 2024) Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$. Hacettepe Journal of Mathematics and Statistics 53 2 417–432.
IEEE Y. Cao ve J. Ruan, “Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$”, Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 2, ss. 417–432, 2024, doi: 10.15672/hujms.1283922.
ISNAD Cao, Yi - Ruan, Jianmiao. “Hermite-Hadamard Type Inequalities for $(p,h)$-Convex Functions on $\mathbb{R}^n$”. Hacettepe Journal of Mathematics and Statistics 53/2 (Nisan 2024), 417-432. https://doi.org/10.15672/hujms.1283922.
JAMA Cao Y, Ruan J. Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$. Hacettepe Journal of Mathematics and Statistics. 2024;53:417–432.
MLA Cao, Yi ve Jianmiao Ruan. “Hermite-Hadamard Type Inequalities for $(p,h)$-Convex Functions on $\mathbb{R}^n$”. Hacettepe Journal of Mathematics and Statistics, c. 53, sy. 2, 2024, ss. 417-32, doi:10.15672/hujms.1283922.
Vancouver Cao Y, Ruan J. Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$. Hacettepe Journal of Mathematics and Statistics. 2024;53(2):417-32.

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