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Year 2015, Volume: 3 Issue: 2, 1 - 19, 30.10.2015
https://doi.org/10.36753/mathenot.421321

Abstract

References

  • [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

Year 2015, Volume: 3 Issue: 2, 1 - 19, 30.10.2015
https://doi.org/10.36753/mathenot.421321

Abstract

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.

References

  • [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 .
There are 16 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Mevlüt Tunç

Ebru Yüksel This is me

Publication Date October 30, 2015
Submission Date January 6, 2015
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

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. October 2015;3(2):1-19. doi:10.36753/mathenot.421321
Chicago Tunç, Mevlüt, and Ebru Yüksel. “SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR S-GEOMETRICALLY CONVEX FUNCTION”. Mathematical Sciences and Applications E-Notes 3, no. 2 (October 2015): 1-19. https://doi.org/10.36753/mathenot.421321.
EndNote Tunç M, Yüksel E (October 1, 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 and E. Yüksel, “SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR s-GEOMETRICALLY CONVEX FUNCTION”, Math. Sci. Appl. E-Notes, vol. 3, no. 2, pp. 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 (October 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 and Ebru Yüksel. “SOME HERMITE-HADAMARD AND SIMPSON LIKE INEQUALITIES FOR S-GEOMETRICALLY CONVEX FUNCTION”. Mathematical Sciences and Applications E-Notes, vol. 3, no. 2, 2015, pp. 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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