Araştırma Makalesi
Yıl 2023,
Cilt: 36 Sayı: 3, 1311 - 1324, 01.09.2023
Öz
In the paper, we introduce the class of trigonometrically convex functions and using the Hölder, Hölder-Işcan, Power-mean and Improved power-mean integral inequality together with an identity we establish some new inequalities of Ostrowski-type for functions whose second derivatives are trigonometrically convex which is a special case of h-convex functions. Some applications for special means are also given.
Anahtar Kelimeler
Ostrowski inequality Hölder-İşcan Improved power-mean Convex trigometrically
Kaynakça
- [1] Ostrowski, A., “Über Die Absolutabweichung einer differentiierbaren funktion von ihrem integralmittelwert”, Commentarii Mathematici Helvetici, 10(1): 226–227, (1938).
- [2] Alomari, M., Darus, M., Dragomir, S.S., Cerone, P., “Ostrowski’s inequalities for functions whose derivatives are s-convex in the second sense”, Applied Mathematics Letters, 23(9): 1071-1076, (2010).
- [3] Cerone, P., Dragomir, S.S., “Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions ”, Demonstratio Mathematica, 37(2): 299-308, (2004).
- [4] Dragomir, S.S., “Some companions of Ostrowski’s inequality for absolutely continuous functions and applications”, Bulletin of the Korean Mathematical Society, 42(2): 213–230, (2005).
- [5] Işcan, I., “Ostrowski type inequalities for functions whose derivatives are preinvex”, Bulletin of the Iranian Mathematical Society, 40(2): 373–386, (2014).
- [6] Sarikaya, M.Z., “On the Ostrowski type integral inequality”, Acta Mathematica Universitatis Comenianae, 79(1): 129-134, (2010).
- [7] Set, E., Ozdemir, M.E., Sarıkaya, M.Z., “New inequalities of Ostrowski’s type for s-convex functions in the second sense with applications”, Facta Universitatis Series Mathematics and Informatics, 27(1): 67–82, (2012).
- [8] Set, E., Ozdemir, M.E., Sarıkaya, M.Z., Akdemir, A.O., “Ostrowski-type inequalities for strongly convex functions”, Georgian Mathematical Journal, 25 (1): 109–115, (2018).
- [9] Ozdemir, M.E., Kavurmacı, H., Set, E., “Ostrowski’s type inequalities for (α,m)-convex functions”, Kyungpook Mathematical Journal, 50(3): 371–378, (2010).
- [10] Hadamard, J. “Étude sur les propriétés des fonctions entières et en particulier d'une fonction considérée par Riemann”, Journal De Mathematiques Pures Et Appliquées, 58: 171-216, (1893).
- [11] Kadakal, M., Kadakal, H., Iscan, I., “Some new integral inequalities for n-times differentiable s-convex functions in the first sense”, Turkish Journal of Analysis and Number Theory, 5(2): 63-68, (2017).
- [12] Maden, S., Kadakal, H., Kadakal, M., Iscan, I., “Some new integral inequalities for n-times differentiable convex and concave functions”, Journal of Nonlinear Sciences and Applications, 10(12): 6141-6148, (2017).
- [13] Varosanec, S., “On h-Convexity”, Journal of Mathematical Analysis and Applications, 326(1): 303-311, (2007).
- [14] Kadakal, H., “Hermite-Hadamard type inequalities for trigonometrically convex functions”, Scientific Studies and Research, Series Mathematics and Informatic, 28(2): 19-28, (2018).
- [15] Işcan, I., “New refinements for integral and sum forms of Hölder inequality”, Journal of Inequalities and Applications, 1: 1-11, (2019).
- [16] Kadakal, M., Işcan, I., Kadakal, H., Bekar, K., “On improvements of some integral inequalities”, Researchgate, (2019). (Preprint) DOI: https://doi.org/10.13140/RG.2.2.15052.46724
- [17] Set, E., Sarikaya, M.Z., Ozdemir, M.E., “Some Ostrowski’s type inequalities for functions whose second derivatives are s-convex in the second sense and applications”, Demonstratio Mathematica, 47(1): 37-47, (2014).
Yıl 2023,
Cilt: 36 Sayı: 3, 1311 - 1324, 01.09.2023
Öz
Kaynakça
- [1] Ostrowski, A., “Über Die Absolutabweichung einer differentiierbaren funktion von ihrem integralmittelwert”, Commentarii Mathematici Helvetici, 10(1): 226–227, (1938).
- [2] Alomari, M., Darus, M., Dragomir, S.S., Cerone, P., “Ostrowski’s inequalities for functions whose derivatives are s-convex in the second sense”, Applied Mathematics Letters, 23(9): 1071-1076, (2010).
- [3] Cerone, P., Dragomir, S.S., “Ostrowski type inequalities for functions whose derivatives satisfy certain convexity assumptions ”, Demonstratio Mathematica, 37(2): 299-308, (2004).
- [4] Dragomir, S.S., “Some companions of Ostrowski’s inequality for absolutely continuous functions and applications”, Bulletin of the Korean Mathematical Society, 42(2): 213–230, (2005).
- [5] Işcan, I., “Ostrowski type inequalities for functions whose derivatives are preinvex”, Bulletin of the Iranian Mathematical Society, 40(2): 373–386, (2014).
- [6] Sarikaya, M.Z., “On the Ostrowski type integral inequality”, Acta Mathematica Universitatis Comenianae, 79(1): 129-134, (2010).
- [7] Set, E., Ozdemir, M.E., Sarıkaya, M.Z., “New inequalities of Ostrowski’s type for s-convex functions in the second sense with applications”, Facta Universitatis Series Mathematics and Informatics, 27(1): 67–82, (2012).
- [8] Set, E., Ozdemir, M.E., Sarıkaya, M.Z., Akdemir, A.O., “Ostrowski-type inequalities for strongly convex functions”, Georgian Mathematical Journal, 25 (1): 109–115, (2018).
- [9] Ozdemir, M.E., Kavurmacı, H., Set, E., “Ostrowski’s type inequalities for (α,m)-convex functions”, Kyungpook Mathematical Journal, 50(3): 371–378, (2010).
- [10] Hadamard, J. “Étude sur les propriétés des fonctions entières et en particulier d'une fonction considérée par Riemann”, Journal De Mathematiques Pures Et Appliquées, 58: 171-216, (1893).
- [11] Kadakal, M., Kadakal, H., Iscan, I., “Some new integral inequalities for n-times differentiable s-convex functions in the first sense”, Turkish Journal of Analysis and Number Theory, 5(2): 63-68, (2017).
- [12] Maden, S., Kadakal, H., Kadakal, M., Iscan, I., “Some new integral inequalities for n-times differentiable convex and concave functions”, Journal of Nonlinear Sciences and Applications, 10(12): 6141-6148, (2017).
- [13] Varosanec, S., “On h-Convexity”, Journal of Mathematical Analysis and Applications, 326(1): 303-311, (2007).
- [14] Kadakal, H., “Hermite-Hadamard type inequalities for trigonometrically convex functions”, Scientific Studies and Research, Series Mathematics and Informatic, 28(2): 19-28, (2018).
- [15] Işcan, I., “New refinements for integral and sum forms of Hölder inequality”, Journal of Inequalities and Applications, 1: 1-11, (2019).
- [16] Kadakal, M., Işcan, I., Kadakal, H., Bekar, K., “On improvements of some integral inequalities”, Researchgate, (2019). (Preprint) DOI: https://doi.org/10.13140/RG.2.2.15052.46724
- [17] Set, E., Sarikaya, M.Z., Ozdemir, M.E., “Some Ostrowski’s type inequalities for functions whose second derivatives are s-convex in the second sense and applications”, Demonstratio Mathematica, 47(1): 37-47, (2014).
Toplam 17 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Mathematics |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Eylül 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 36 Sayı: 3 |