Öz
In this paper, we first construct a new generalization of $n$-polynomial convex function. That is, this study is a generalization of the definition of "$n$-polynomial convexity" previously found in the literature. By making use of this construction, we derive certain inequalities for this new generalization and show that the first derivative in absolute value corresponds to a new class of $n$-polynomial convexity. Also, we see that the obtained results in the paper while comparing with Hölder, Hölder-İşcan and power-mean, improved-power-mean integral inequalities show that the results give a better approach than the others. Finally, we conclude our paper with applications containing some means.
Anahtar Kelimeler
convex function n-polynomial convexity generalized n-polynomial convexity Hermite-Hadamard inequality Hölder-İşcan integral inequality
Kaynakça
- [1] P. Agarwal, M. Kadakal, İ. İşcan and Y.M. Chu, Better approaches for n-times differentiable convex functions, Mathematics, 8 (6), 950, 2020.
- [2] M. Bombardelli and S. Varošanec, Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities, Comput. Math. Appl. 58, 1869-1877, 2009.
- [3] S.I. Butt, P. Agarwal, S. Yousaf and J. L. Guirao, Generalized fractal Jensen and Jensen-Mercer inequalities for harmonic convex function with applications, J. Inequal. Appl. 2022 (1), 1-18, 2022.
- [4] S.S. Dragomir and RP Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11, 91-95, 1998.
- [5] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Its Applications, RGMIA Monograph , 2002.
- [6] J. Hadamard, Étude sur les propriétés des fonctions entières en particulier d’une fonction considérée par Riemann, J. Math. Pures Appl. 58, 171-215, 1893.
- [7] İ. İşcan, New refinements for integral and sum forms of Hölder inequality, J. Inequal. Appl. 2019 (1), 1-11, 2019.
- [8] S. Jain, K. Mehrez, D. Baleanu and P. Agarwal, Certain Hermite-Hadamard inequalities for logarithmically convex functions with applications, Mathematics, 7 (2), 163, 2019.
- [9] H. Kadakal, Hermite-Hadamard type inequalities for trigonometrically convex functions, Sci. Stud. Res. Ser. Math. Inform. 28 (2), 19-28, 2018.
- [10] M. Kadakal, İ. İşcan, H. Kadakal and K. Bekar, On improvements of some integral inequalities, Honam Math. J. 43 (3), 441-452, 2021.
- [11] M. Khaled and P. Agarwal, New Hermite-Hadamard type integral inequalities for convex functions and their applications, J. Comput. Appl. Math. 350, 274-285, 2019.
- [12] C.E.M. Pearce and J. Pečarić, Inequalities for differentiable mappings with application to special means and Quadrature formulae, Appl. Math. Lett. 13, 51-55, 2000.
- [13] T. Toplu, M. Kadakal and İ. İşcan, On n-Polynomial convexity and some related inequalities, AIMS Mathematics, 5 (2), 1304-1318, 2020.
- [14] S. Varošanec, On h-convexity, J. Math. Anal. Appl. 326, 303-311, 2007.
- [15] M. Vivas-Cortez, M. A. Ali, H. Budak, H. Kalsoom and P. Agarwal, Some new Hermite-Hadamard and related inequalities for convex functions via (p, q)-integral, Entropy, 23 (7), 828, 2021.
- [16] G. Zabandan, A new refinement of the Hermite-Hadamard inequality for convex functions, J. Inequal. Pure Appl. Math. 10 (2), Article ID 45, 2009.
Öz
Kaynakça
- [1] P. Agarwal, M. Kadakal, İ. İşcan and Y.M. Chu, Better approaches for n-times differentiable convex functions, Mathematics, 8 (6), 950, 2020.
- [2] M. Bombardelli and S. Varošanec, Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities, Comput. Math. Appl. 58, 1869-1877, 2009.
- [3] S.I. Butt, P. Agarwal, S. Yousaf and J. L. Guirao, Generalized fractal Jensen and Jensen-Mercer inequalities for harmonic convex function with applications, J. Inequal. Appl. 2022 (1), 1-18, 2022.
- [4] S.S. Dragomir and RP Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11, 91-95, 1998.
- [5] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Its Applications, RGMIA Monograph , 2002.
- [6] J. Hadamard, Étude sur les propriétés des fonctions entières en particulier d’une fonction considérée par Riemann, J. Math. Pures Appl. 58, 171-215, 1893.
- [7] İ. İşcan, New refinements for integral and sum forms of Hölder inequality, J. Inequal. Appl. 2019 (1), 1-11, 2019.
- [8] S. Jain, K. Mehrez, D. Baleanu and P. Agarwal, Certain Hermite-Hadamard inequalities for logarithmically convex functions with applications, Mathematics, 7 (2), 163, 2019.
- [9] H. Kadakal, Hermite-Hadamard type inequalities for trigonometrically convex functions, Sci. Stud. Res. Ser. Math. Inform. 28 (2), 19-28, 2018.
- [10] M. Kadakal, İ. İşcan, H. Kadakal and K. Bekar, On improvements of some integral inequalities, Honam Math. J. 43 (3), 441-452, 2021.
- [11] M. Khaled and P. Agarwal, New Hermite-Hadamard type integral inequalities for convex functions and their applications, J. Comput. Appl. Math. 350, 274-285, 2019.
- [12] C.E.M. Pearce and J. Pečarić, Inequalities for differentiable mappings with application to special means and Quadrature formulae, Appl. Math. Lett. 13, 51-55, 2000.
- [13] T. Toplu, M. Kadakal and İ. İşcan, On n-Polynomial convexity and some related inequalities, AIMS Mathematics, 5 (2), 1304-1318, 2020.
- [14] S. Varošanec, On h-convexity, J. Math. Anal. Appl. 326, 303-311, 2007.
- [15] M. Vivas-Cortez, M. A. Ali, H. Budak, H. Kalsoom and P. Agarwal, Some new Hermite-Hadamard and related inequalities for convex functions via (p, q)-integral, Entropy, 23 (7), 828, 2021.
- [16] G. Zabandan, A new refinement of the Hermite-Hadamard inequality for convex functions, J. Inequal. Pure Appl. Math. 10 (2), Article ID 45, 2009.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Reel ve Kompleks Fonksiyonlar |
| Bölüm | Matematik |
| Yazarlar | |
| Erken Görünüm Tarihi | 10 Ocak 2024 |
| Yayımlanma Tarihi | 28 Aralık 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 53 Sayı: 6 |