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BibTex RIS Kaynak Göster
Yıl 2015, Cilt: 3 Sayı: 2, 1 - 19, 30.10.2015
https://doi.org/10.36753/mathenot.421321

Öz

Kaynakça

  • [1] Alomari, M., Darus, M., Dragomir, S. S., New inequalities of Simpson’s type for sconvex functions with applications. RGMIA Res. Rep. Coll. 12 (4) (2009) Article 9. Online http://ajmaa.org/RGMIA/v12n4.php.
  • [2] Alomari, M., Darus, M., Kırmacı, U. S., Refinements of Hadamard-type inequalities for quasiconvex functions with applications to trapezoidal formula and to special means, Comp. and Math. with Appl. Vol.59 (2010), 225-232.
  • [3] Bai, R.-F., Qi, F., Xi, B.-Y., Hermite-Hadamard type inequalities for the m- and (α, m)- logarithmically convex functions. Filomat, 27 (2013), 1-7.
  • [4] Dragomir, S. S., Agarwal, R. P., Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998) no. 5, 91-95.
  • [5] Dragomir, S. S., Agarwal, R. P., Cerone, P., On Simpson’s inequality and applications. J. of Ineq. and Appl., 5 (2000), 533-579.
  • [6] Dragomir, S. S., Pearce, C. E. M., Selected topics on Hermite-Hadamard inequalities and applications, RGMIA monographs, Victoria University, 2000. [Online:http://www.staff.vu.edu.au/RGMIA/monographs/hermite-hadamard.html].
  • [7] Hadamard, J., Etude sur les propri´et´es des fonctions enti`eres et en particulier d’une fonction ´ consider´ee par Riemann. J. Math Pures Appl., 58, (1893) 171-215.
  • [8] Hudzik, H., Maligranda, L., Some remarks on s-convex functions. Aequationes Math., Vol. 48 (1994), 100-111.
  • [9] Mitrinovic, D. S., Pecaric, J., Fink,A. M., Classical and new inequalities in analysis. KluwerAcademic, Dordrecht, 1993.
  • [10] Pecari´c, J. E., Proschan, F. Tong, Y. L., Convex Functions, Partial Orderings, and Statistical Applications. Academic Press Inc., 1992.
  • [11] Sarikaya, M. Z., Set, E., Ozdemir, M.E., On new inequalities of Simpson’s type for convex ¨ functions. RGMIA Res. Rep. Coll. 13 (2) (2010) Article2.
  • [12] Sarikaya, M. Z., Set, E., Ozdemir, M.E., On new inequalities of Simpson’s type for ¨ s-convex functions. Comp. and Math. with Appl. 60 (2010) 2191-2199.
  • [13] Tunç, M., On some new inequalities for convex functions. Turk. J. Math. 36 (2012), 245-251.
  • [14] Xi, B.-Y., Qi, F., Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means. Journal of Function Spaces and Appl., Volume 2012, Article ID 980438, 14 p., doi:10.1155/2012/980438.
  • [15] Zhang, T.-Y., Ji, A.-P., Qi, F., On integral inequalities of Hermite-Hadamard type for sgeometrically convex function. Abstract and Applied Analysis, doi:10.1155/2012/560586.
  • [16] Zhang, T.-Y., Tunç, M., Ji, A.-P., Xi, B.-Y., Corrections to the paper ”On integral inequalities of Hermite-Hadamard type for s-geometrically convex function”. Abstract and Applied Analysis, (2014), Article ID 294739, http://dx.doi.org/10.1155/2014/294739 .

SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR s-GEOMETRICALLY CONVEX FUNCTION

Yıl 2015, Cilt: 3 Sayı: 2, 1 - 19, 30.10.2015
https://doi.org/10.36753/mathenot.421321

Öz

In the paper, the authors establish and generalize some new integral
inequalities of Hermite-Hadamard and Simpson type for functions the
power of the absolute of whose first derivative is s-geometrically convex.

Kaynakça

  • [1] Alomari, M., Darus, M., Dragomir, S. S., New inequalities of Simpson’s type for sconvex functions with applications. RGMIA Res. Rep. Coll. 12 (4) (2009) Article 9. Online http://ajmaa.org/RGMIA/v12n4.php.
  • [2] Alomari, M., Darus, M., Kırmacı, U. S., Refinements of Hadamard-type inequalities for quasiconvex functions with applications to trapezoidal formula and to special means, Comp. and Math. with Appl. Vol.59 (2010), 225-232.
  • [3] Bai, R.-F., Qi, F., Xi, B.-Y., Hermite-Hadamard type inequalities for the m- and (α, m)- logarithmically convex functions. Filomat, 27 (2013), 1-7.
  • [4] Dragomir, S. S., Agarwal, R. P., Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998) no. 5, 91-95.
  • [5] Dragomir, S. S., Agarwal, R. P., Cerone, P., On Simpson’s inequality and applications. J. of Ineq. and Appl., 5 (2000), 533-579.
  • [6] Dragomir, S. S., Pearce, C. E. M., Selected topics on Hermite-Hadamard inequalities and applications, RGMIA monographs, Victoria University, 2000. [Online:http://www.staff.vu.edu.au/RGMIA/monographs/hermite-hadamard.html].
  • [7] Hadamard, J., Etude sur les propri´et´es des fonctions enti`eres et en particulier d’une fonction ´ consider´ee par Riemann. J. Math Pures Appl., 58, (1893) 171-215.
  • [8] Hudzik, H., Maligranda, L., Some remarks on s-convex functions. Aequationes Math., Vol. 48 (1994), 100-111.
  • [9] Mitrinovic, D. S., Pecaric, J., Fink,A. M., Classical and new inequalities in analysis. KluwerAcademic, Dordrecht, 1993.
  • [10] Pecari´c, J. E., Proschan, F. Tong, Y. L., Convex Functions, Partial Orderings, and Statistical Applications. Academic Press Inc., 1992.
  • [11] Sarikaya, M. Z., Set, E., Ozdemir, M.E., On new inequalities of Simpson’s type for convex ¨ functions. RGMIA Res. Rep. Coll. 13 (2) (2010) Article2.
  • [12] Sarikaya, M. Z., Set, E., Ozdemir, M.E., On new inequalities of Simpson’s type for ¨ s-convex functions. Comp. and Math. with Appl. 60 (2010) 2191-2199.
  • [13] Tunç, M., On some new inequalities for convex functions. Turk. J. Math. 36 (2012), 245-251.
  • [14] Xi, B.-Y., Qi, F., Some Integral Inequalities of Hermite-Hadamard Type for Convex Functions with Applications to Means. Journal of Function Spaces and Appl., Volume 2012, Article ID 980438, 14 p., doi:10.1155/2012/980438.
  • [15] Zhang, T.-Y., Ji, A.-P., Qi, F., On integral inequalities of Hermite-Hadamard type for sgeometrically convex function. Abstract and Applied Analysis, doi:10.1155/2012/560586.
  • [16] Zhang, T.-Y., Tunç, M., Ji, A.-P., Xi, B.-Y., Corrections to the paper ”On integral inequalities of Hermite-Hadamard type for s-geometrically convex function”. Abstract and Applied Analysis, (2014), Article ID 294739, http://dx.doi.org/10.1155/2014/294739 .
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Mevlüt Tunç

Ebru Yüksel Bu kişi benim

Yayımlanma Tarihi 30 Ekim 2015
Gönderilme Tarihi 6 Ocak 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 2

Kaynak Göster

APA Tunç, M., & Yüksel, E. (2015). SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR s-GEOMETRICALLY CONVEX FUNCTION. Mathematical Sciences and Applications E-Notes, 3(2), 1-19. https://doi.org/10.36753/mathenot.421321
AMA Tunç M, Yüksel E. SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR s-GEOMETRICALLY CONVEX FUNCTION. Math. Sci. Appl. E-Notes. Ekim 2015;3(2):1-19. doi:10.36753/mathenot.421321
Chicago Tunç, Mevlüt, ve Ebru Yüksel. “SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR S-GEOMETRICALLY CONVEX FUNCTION”. Mathematical Sciences and Applications E-Notes 3, sy. 2 (Ekim 2015): 1-19. https://doi.org/10.36753/mathenot.421321.
EndNote Tunç M, Yüksel E (01 Ekim 2015) SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR s-GEOMETRICALLY CONVEX FUNCTION. Mathematical Sciences and Applications E-Notes 3 2 1–19.
IEEE M. Tunç ve E. Yüksel, “SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR s-GEOMETRICALLY CONVEX FUNCTION”, Math. Sci. Appl. E-Notes, c. 3, sy. 2, ss. 1–19, 2015, doi: 10.36753/mathenot.421321.
ISNAD Tunç, Mevlüt - Yüksel, Ebru. “SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR S-GEOMETRICALLY CONVEX FUNCTION”. Mathematical Sciences and Applications E-Notes 3/2 (Ekim 2015), 1-19. https://doi.org/10.36753/mathenot.421321.
JAMA Tunç M, Yüksel E. SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR s-GEOMETRICALLY CONVEX FUNCTION. Math. Sci. Appl. E-Notes. 2015;3:1–19.
MLA Tunç, Mevlüt ve Ebru Yüksel. “SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR S-GEOMETRICALLY CONVEX FUNCTION”. Mathematical Sciences and Applications E-Notes, c. 3, sy. 2, 2015, ss. 1-19, doi:10.36753/mathenot.421321.
Vancouver Tunç M, Yüksel E. SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR s-GEOMETRICALLY CONVEX FUNCTION. Math. Sci. Appl. E-Notes. 2015;3(2):1-19.

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