Research Article
BibTex RIS Cite

Year 2019, Volume: 68 Issue: 2, 2128 - 2142, 01.08.2019

Huriye Kadakal

https://doi.org/10.31801/cfsuasmas.511184
Cited By: 7

Abstract

References

  • Bakula, M. K., Özdemir, M. E. and Pečarić, J. Hadamard tpye inequalities for m-convex and (α,m) -convex functions, J. Inequal. Pure and Appl. Math., 9(4)(2008), 1-25.
  • Dragomir, S.S. On Some New Inequalities of Hermite-Hadamard Type for m-Convex Functions, Tamkang Journal of Mathematics, Volume 33, Number 1, Spring 2002, 45--55.
  • Dragomir, S.S. and Pearce, CEM. Selected Topics on Hermite-Hadamard Inequalities and Its Applications, RGMIA Monograph (2002).
  • Kadakal, H., (m₁,m₂)-convexity and some new Hermite-Hadamard type inequalities, Journal of Applied and Engineering Mathematics, (accepted for publications), 2019.
  • Kavurmaci, H., Avci M. and Özdemir, M.E. New inequalities of Hermite-Hadamard type for convex functions with applications, Journal of Inequalities and Applications, 2011, 2011:86.
  • Kirmaci, U. S., Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. and Comput., 147 (2004) 137--146.
  • Kırmacı, U. S., Bakula, M. K., Özdemir, M. E. and Pe čarić, J. Hadamard-tpye inequalities for s-convex functions, Appl. Math. and Comp., 193(2007), 26--35.
  • Lara, T., Rosales, E. and Sánchez, J.L. New Properties of m-Convex Functions, International Journal of Mathematical Analysis, Vol. 9, 2015, No. 15, 735--742.
  • Mihaly, B. Hermite-Hadamard-type inequalities for generalized convex functions. J. Inequal, Pure Appl. Math., 9(3), Article ID 63 (2008) (PhD thesis).
  • Özdemir, M. E., Latif M. A. and Akdemir, A. O. On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates, Journal of Inequalities and Applications, 2012, 2012:21.
  • Özdemir, M. E., Set E. and Sarıkaya, M. Z. Some new Hadamard's type inequalities for co-ordinated m-convex and (α,m)-convex functions, Hacettepe J. of. Math. and Statistics, 40(2011), 219--229.
  • Park, J., New Ostrowski-Like type inequalities for differentiable (s,m)-convex mappings, International Journal of Pure and Applied Mathematics, Volume 78 No. 8 2012, 1077--1089.
  • Pečarić, J. E., Proschan, F and Tong, Y. L. Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, INC, 1992.
  • Sarikaya, M.Z., Sağlam A. and Yıldırım, H. On some Hadamard-type inequalities for h-convex functions, J. Math. Ineq., 2(3)(2008), 335--341.
  • Toader, G. The hierarchy of convexity and some classic inequalities, J. Math. Ineq.,3(3)(2009), 305--313.

(alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type

Year 2019, Volume: 68 Issue: 2, 2128 - 2142, 01.08.2019

Huriye Kadakal

https://doi.org/10.31801/cfsuasmas.511184
Cited By: 7

Abstract

In this paper, we introduce a new class of extended (alpha;m1;m2)-convex functions. Some algebraic properties of these class functions have been investigated. Some new Hermite-Hadamard type inequalities are derived. Results represent signicant refinement and improvement of the previous results. Also, the author establish a new integral identity and, by this identity, Hölder's and power mean inequality, discover some new Hermite-Hadamard type inequalities for functions whose first derivatives are (alpha;m1;m2)-convex. Our results are new and coincide with the previous results in special cases.

Keywords

Convex function m-Convex function (alpha;m)-Convex function (alpha;m1;m2)-Convex function Hermite-Hadamard type inequality

References

  • Bakula, M. K., Özdemir, M. E. and Pečarić, J. Hadamard tpye inequalities for m-convex and (α,m) -convex functions, J. Inequal. Pure and Appl. Math., 9(4)(2008), 1-25.
  • Dragomir, S.S. On Some New Inequalities of Hermite-Hadamard Type for m-Convex Functions, Tamkang Journal of Mathematics, Volume 33, Number 1, Spring 2002, 45--55.
  • Dragomir, S.S. and Pearce, CEM. Selected Topics on Hermite-Hadamard Inequalities and Its Applications, RGMIA Monograph (2002).
  • Kadakal, H., (m₁,m₂)-convexity and some new Hermite-Hadamard type inequalities, Journal of Applied and Engineering Mathematics, (accepted for publications), 2019.
  • Kavurmaci, H., Avci M. and Özdemir, M.E. New inequalities of Hermite-Hadamard type for convex functions with applications, Journal of Inequalities and Applications, 2011, 2011:86.
  • Kirmaci, U. S., Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. and Comput., 147 (2004) 137--146.
  • Kırmacı, U. S., Bakula, M. K., Özdemir, M. E. and Pe čarić, J. Hadamard-tpye inequalities for s-convex functions, Appl. Math. and Comp., 193(2007), 26--35.
  • Lara, T., Rosales, E. and Sánchez, J.L. New Properties of m-Convex Functions, International Journal of Mathematical Analysis, Vol. 9, 2015, No. 15, 735--742.
  • Mihaly, B. Hermite-Hadamard-type inequalities for generalized convex functions. J. Inequal, Pure Appl. Math., 9(3), Article ID 63 (2008) (PhD thesis).
  • Özdemir, M. E., Latif M. A. and Akdemir, A. O. On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates, Journal of Inequalities and Applications, 2012, 2012:21.
  • Özdemir, M. E., Set E. and Sarıkaya, M. Z. Some new Hadamard's type inequalities for co-ordinated m-convex and (α,m)-convex functions, Hacettepe J. of. Math. and Statistics, 40(2011), 219--229.
  • Park, J., New Ostrowski-Like type inequalities for differentiable (s,m)-convex mappings, International Journal of Pure and Applied Mathematics, Volume 78 No. 8 2012, 1077--1089.
  • Pečarić, J. E., Proschan, F and Tong, Y. L. Convex Functions, Partial Orderings, and Statistical Applications, Academic Press, INC, 1992.
  • Sarikaya, M.Z., Sağlam A. and Yıldırım, H. On some Hadamard-type inequalities for h-convex functions, J. Math. Ineq., 2(3)(2008), 335--341.
  • Toader, G. The hierarchy of convexity and some classic inequalities, J. Math. Ineq.,3(3)(2009), 305--313.
There are 15 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Review Articles
Authors

Huriye Kadakal 0000-0002-0304-7192

Publication Date August 1, 2019
Submission Date January 10, 2019
Acceptance Date May 31, 2019
Published in Issue Year 2019 Volume: 68 Issue: 2

Cite

APA Kadakal, H. (2019). (alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 2128-2142. https://doi.org/10.31801/cfsuasmas.511184
AMA Kadakal H. (alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):2128-2142. doi:10.31801/cfsuasmas.511184
Chicago Kadakal, Huriye. “(alpha,m1,m2)-Convexity and Some Inequalities of Hermite-Hadamard Type”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 2128-42. https://doi.org/10.31801/cfsuasmas.511184.
EndNote Kadakal H (August 1, 2019) (alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 2128–2142.
IEEE H. Kadakal, “(alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 2128–2142, 2019, doi: 10.31801/cfsuasmas.511184.
ISNAD Kadakal, Huriye. “(alpha,m1,m2)-Convexity and Some Inequalities of Hermite-Hadamard Type”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 2128-2142. https://doi.org/10.31801/cfsuasmas.511184.
JAMA Kadakal H. (alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:2128–2142.
MLA Kadakal, Huriye. “(alpha,m1,m2)-Convexity and Some Inequalities of Hermite-Hadamard Type”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 2128-42, doi:10.31801/cfsuasmas.511184.
Vancouver Kadakal H. (alpha,m1,m2)-convexity and some inequalities of Hermite-Hadamard type. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):2128-42.

Cited By

On $ \psi $-convex functions and related inequalities
AIMS Mathematics
https://doi.org/10.3934/math.2024546
A generalization of convexity via an implicit inequality
AIMS Mathematics
https://doi.org/10.3934/math.2024586
Applications of Hölder-İşcan inequality for $ n $-times differentiable $ (s, m) $-convex functions
AIMS Mathematics
https://doi.org/10.3934/math.2023082
Some new inequalities for (α,m1,m2 )-GA convex functions
Sakarya University Journal of Science
https://doi.org/10.16984/saufenbilder.699212
Hermite–Hadamard type inequalities for m-convex and $( \alpha , m)$-convex functions
Journal of Inequalities and Applications
https://doi.org/10.1186/s13660-020-02442-5
Generalization of Some Integral Inequalities for Arithmetic Harmonically Convex Functions
Cumhuriyet Science Journal
https://doi.org/10.17776/csj.1110051
Better Approaches for n-Times Differentiable Convex Functions
Mathematics
https://doi.org/10.3390/math8060950

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.