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Generalized Hermite-Hadamard type inequalities for products of co-ordinated convex functions

Year 2020, Volume: 69 Issue: 1, 863 - 879, 30.06.2020

Hüseyin Budak Tuba Tunç

https://doi.org/10.31801/cfsuasmas.600814
Cited By: 2

Abstract

In this paper, we think products of two co-ordinated convex functions for the Hermite-Hadamard type inequalities. Using these functions we obtained Hermite-Hadamard type inequalities which are generalizations of some results given in earlier works.

Keywords

Hermite-Hadamard's inequalities co-ordinated convex

References

  • Akkurt, A., Sarikaya, M. Z., Budak, H., Yildirim, H., On the Hadamard's type inequalities for co-ordinated convex functions via fractional integrals, Journal of King Saud University-Science, 29(2017), 380-387.
  • Alomari, M., Darus, M., The Hadamards inequality for s-convex function of 2-variables on the coordinates, Int. J. Math. Anal., 2(13) (2008), 629-638.
  • Alomari, M., Darus, M., On the Hadamard's inequality for log-convex functions on the coordinates, Journal of Inequalities and Applications, vol.2009, Article ID 283147, 13 pages.
  • Azpeitia, A. G., Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28(1994), 7-12.
  • Bakula, M. K., An improvement of the Hermite-Hadamard inequality for functions convex on the coordinates, Australian Journal of Mathematical Analysis and Applications, 11(1) (2014), 1-7.
  • Budak, H., Sarıkaya, M. Z., Hermite-Hadamard type inequalities for products of two co-ordinated convex mappings via fractional integrals, International Journal of Applied Mathematics and Statistics, 58(4) (2019), 11-30.
  • Budak, H., Bakış, Y., On Fejer type inequalities for products two convex functions, Note Di Matematica, in press.
  • Chen, F., On Hermite-Hadamard type inequalities for s-convex functions on the coordinates via Riemann-Liouville fractional integrals, Journal of Applied Mathematics, vol. 2014, Article ID 248710, 8 pages.
  • Chen, F., A note on Hermite-Hadamard inequalities for products of convex functions via Riemann-Liouville fractional integrals, Ital. J. Pure Appl. Math., 33(2014), 299-306.
  • Chen, F., A note on Hermite-Hadamard inequalities for products of convex functions, Journal of Applied Mathematics, vol. 2013, Article ID 935020, 5 pages.
  • Chen, F., ,Wu, S., Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl., 9 (2016), 705-716.
  • Dragomir, S. S., On Hadamards inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwan. J. Math., 4(2001), 775-788 .
  • Dragomir, S. S. and Pearce, C. E. M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • Dragomir, S. S., Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Proyecciones J. Math., 37(4) (2015), 343-341 .
  • Erden, S., Sarikaya, M. Z., On the Hermite-Hadamard-type and Ostrowski-type inequalities for the co-ordinated convex functions, Palestine Journal of Mathematics, 6 (1)(2017), 257-270.
  • Erden, S., Sarıkaya, M. Z., On the Hermite-Hadamard's and Ostrowski's inequalities for the co-ordinated convex functions, New Trends in Mathematical Sciences, NTMSCI, 5(3)(2017), 33-45.
  • Kırmacı, U. S., Bakula, M. K., Özdemir, M. E., Pečarić ,J., Hadamard-type inequalities for s-convex functions, Appl. Math. Comput., 193(2007), 26-35.
  • Latif, M. A., Alomari, M., Hadamard-type inequalities for product two convex functions on the co-ordinates, Int. Math. Forum., 4(47) (2009), 2327-2338.
  • Latif, M. A., Hermite-Hadamard type inequalities for GA-convex functions on the co-ordinates with applications, Proceedings of the Pakistan Academy of Science, 52(4) (2015), 367-379.
  • Meftah, B., Souahi, A., Fractional Hermite-Hadamard type inequalities for co-ordinated Mt-convex functions, Turkish J. Ineq., 2(1) (2018), 76 -86.
  • Ozdemir, M. E., Yildiz, C., Akdemir, A. O., On the co-ordinated convex functions, Appl. Math. Inf. Sci., 8(3) (2014), 1085-1091.
  • Ozdemir, M. E., Latif, M. A., Akdemir, A. O., On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates, J.Inequal. Appl., 21(2012), 1-13.
  • Ozdemir, M. E., Latif, M. A., Akdemir, A. O., On some Hadamard-type inequalities for product of two h-convex functions on the co-ordinates, Turkish Journal of Science, 1(2016), 41-58.
  • Pachpatte, B. G., On some inequalities for convex functions, RGMIA Res. Rep. Coll., 6 (E) (2003).
  • Pavic, Z., Improvements of the Hermite-Hadamard inequality, Journal of Inequalities and Applications, (2015), 2015:222.
  • Pečarić, J. E., Proschan, F., Tong, L., Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
  • Sarikaya, M. Z., Set, E., Yaldiz, H., Basak, N., Hermite -Hadamard's inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57 (2013), 2403-2407.
  • Sarikaya, M. Z., On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms and Special Functions, 25(2) (2014), 134-147.
  • Set, E., Özdemir, M. E., Dragomir, S. S., On the Hermite-Hadamard inequality and other integral inequalities involving two functions, J. Inequal. Appl., vol. 2010, Article ID 148102, 9 pages.
  • Set, E., Choi, J., Çelik, B. , New Hermite-Hadamard type inequalities for product of different convex functions involving certain fractional integral operators, Journal of Mathematics and Computer Science, 18(1) (2018), 29-36.
  • Wang, D. Y., Tseng, K. L., Yang, G. S., Some Hadamard's inequalities for co-ordinated convex functions in a rectangle from the plane, Taiwan. J. Math., 11(2007), 63-73.
  • Xi, B. Y., Hua, J., Qi, F., Hermite-Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle, J. Appl. Anal., 20(1) (2014), 1-17.
  • Yaldiz, H., Sarıkaya, M. Z., Dahmani, Z., On the Hermite-Hadamard-Fejer-type inequalities for co-ordinated convex functions via fractional integrals, International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7(2) (2017), 205-215.
  • Yang, G. S., Tseng, K. L., On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239(1999), 180-187.
  • Yang, G. S., Hong, M. C., A note on Hadamard's inequality, Tamkang J. Math., 28(1997), 33-37.
  • Yıldırım, M. E., Akkurt, A., Yıldırım, H., Hermite-Hadamard type inequalities for co-ordinated (α₁,m₁)-(α₂,m₂)-convex functions via fractional integrals, Contemporary Analysis and Applied Mathematics, 4(1) (2016), 48-63.
  • Yin, H. P., Qi, F., Hermite-Hadamard type inequalities for the product of (α,m)-convex functions, J. Nonlinear Sci. Appl., 8(2015), 231-236.

Year 2020, Volume: 69 Issue: 1, 863 - 879, 30.06.2020

Hüseyin Budak Tuba Tunç

https://doi.org/10.31801/cfsuasmas.600814
Cited By: 2

Abstract

References

  • Akkurt, A., Sarikaya, M. Z., Budak, H., Yildirim, H., On the Hadamard's type inequalities for co-ordinated convex functions via fractional integrals, Journal of King Saud University-Science, 29(2017), 380-387.
  • Alomari, M., Darus, M., The Hadamards inequality for s-convex function of 2-variables on the coordinates, Int. J. Math. Anal., 2(13) (2008), 629-638.
  • Alomari, M., Darus, M., On the Hadamard's inequality for log-convex functions on the coordinates, Journal of Inequalities and Applications, vol.2009, Article ID 283147, 13 pages.
  • Azpeitia, A. G., Convex functions and the Hadamard inequality, Rev. Colombiana Math., 28(1994), 7-12.
  • Bakula, M. K., An improvement of the Hermite-Hadamard inequality for functions convex on the coordinates, Australian Journal of Mathematical Analysis and Applications, 11(1) (2014), 1-7.
  • Budak, H., Sarıkaya, M. Z., Hermite-Hadamard type inequalities for products of two co-ordinated convex mappings via fractional integrals, International Journal of Applied Mathematics and Statistics, 58(4) (2019), 11-30.
  • Budak, H., Bakış, Y., On Fejer type inequalities for products two convex functions, Note Di Matematica, in press.
  • Chen, F., On Hermite-Hadamard type inequalities for s-convex functions on the coordinates via Riemann-Liouville fractional integrals, Journal of Applied Mathematics, vol. 2014, Article ID 248710, 8 pages.
  • Chen, F., A note on Hermite-Hadamard inequalities for products of convex functions via Riemann-Liouville fractional integrals, Ital. J. Pure Appl. Math., 33(2014), 299-306.
  • Chen, F., A note on Hermite-Hadamard inequalities for products of convex functions, Journal of Applied Mathematics, vol. 2013, Article ID 935020, 5 pages.
  • Chen, F., ,Wu, S., Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions, J. Nonlinear Sci. Appl., 9 (2016), 705-716.
  • Dragomir, S. S., On Hadamards inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwan. J. Math., 4(2001), 775-788 .
  • Dragomir, S. S. and Pearce, C. E. M., Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.
  • Dragomir, S. S., Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Proyecciones J. Math., 37(4) (2015), 343-341 .
  • Erden, S., Sarikaya, M. Z., On the Hermite-Hadamard-type and Ostrowski-type inequalities for the co-ordinated convex functions, Palestine Journal of Mathematics, 6 (1)(2017), 257-270.
  • Erden, S., Sarıkaya, M. Z., On the Hermite-Hadamard's and Ostrowski's inequalities for the co-ordinated convex functions, New Trends in Mathematical Sciences, NTMSCI, 5(3)(2017), 33-45.
  • Kırmacı, U. S., Bakula, M. K., Özdemir, M. E., Pečarić ,J., Hadamard-type inequalities for s-convex functions, Appl. Math. Comput., 193(2007), 26-35.
  • Latif, M. A., Alomari, M., Hadamard-type inequalities for product two convex functions on the co-ordinates, Int. Math. Forum., 4(47) (2009), 2327-2338.
  • Latif, M. A., Hermite-Hadamard type inequalities for GA-convex functions on the co-ordinates with applications, Proceedings of the Pakistan Academy of Science, 52(4) (2015), 367-379.
  • Meftah, B., Souahi, A., Fractional Hermite-Hadamard type inequalities for co-ordinated Mt-convex functions, Turkish J. Ineq., 2(1) (2018), 76 -86.
  • Ozdemir, M. E., Yildiz, C., Akdemir, A. O., On the co-ordinated convex functions, Appl. Math. Inf. Sci., 8(3) (2014), 1085-1091.
  • Ozdemir, M. E., Latif, M. A., Akdemir, A. O., On some Hadamard-type inequalities for product of two s-convex functions on the co-ordinates, J.Inequal. Appl., 21(2012), 1-13.
  • Ozdemir, M. E., Latif, M. A., Akdemir, A. O., On some Hadamard-type inequalities for product of two h-convex functions on the co-ordinates, Turkish Journal of Science, 1(2016), 41-58.
  • Pachpatte, B. G., On some inequalities for convex functions, RGMIA Res. Rep. Coll., 6 (E) (2003).
  • Pavic, Z., Improvements of the Hermite-Hadamard inequality, Journal of Inequalities and Applications, (2015), 2015:222.
  • Pečarić, J. E., Proschan, F., Tong, L., Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.
  • Sarikaya, M. Z., Set, E., Yaldiz, H., Basak, N., Hermite -Hadamard's inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57 (2013), 2403-2407.
  • Sarikaya, M. Z., On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms and Special Functions, 25(2) (2014), 134-147.
  • Set, E., Özdemir, M. E., Dragomir, S. S., On the Hermite-Hadamard inequality and other integral inequalities involving two functions, J. Inequal. Appl., vol. 2010, Article ID 148102, 9 pages.
  • Set, E., Choi, J., Çelik, B. , New Hermite-Hadamard type inequalities for product of different convex functions involving certain fractional integral operators, Journal of Mathematics and Computer Science, 18(1) (2018), 29-36.
  • Wang, D. Y., Tseng, K. L., Yang, G. S., Some Hadamard's inequalities for co-ordinated convex functions in a rectangle from the plane, Taiwan. J. Math., 11(2007), 63-73.
  • Xi, B. Y., Hua, J., Qi, F., Hermite-Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle, J. Appl. Anal., 20(1) (2014), 1-17.
  • Yaldiz, H., Sarıkaya, M. Z., Dahmani, Z., On the Hermite-Hadamard-Fejer-type inequalities for co-ordinated convex functions via fractional integrals, International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7(2) (2017), 205-215.
  • Yang, G. S., Tseng, K. L., On certain integral inequalities related to Hermite-Hadamard inequalities, J. Math. Anal. Appl., 239(1999), 180-187.
  • Yang, G. S., Hong, M. C., A note on Hadamard's inequality, Tamkang J. Math., 28(1997), 33-37.
  • Yıldırım, M. E., Akkurt, A., Yıldırım, H., Hermite-Hadamard type inequalities for co-ordinated (α₁,m₁)-(α₂,m₂)-convex functions via fractional integrals, Contemporary Analysis and Applied Mathematics, 4(1) (2016), 48-63.
  • Yin, H. P., Qi, F., Hermite-Hadamard type inequalities for the product of (α,m)-convex functions, J. Nonlinear Sci. Appl., 8(2015), 231-236.
There are 37 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Hüseyin Budak 0000-0001-8843-955X

Tuba Tunç 0000-0002-4155-9180

Publication Date June 30, 2020
Submission Date August 2, 2019
Acceptance Date April 24, 2020
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Budak, H., & Tunç, T. (2020). Generalized Hermite-Hadamard type inequalities for products of co-ordinated convex functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 863-879. https://doi.org/10.31801/cfsuasmas.600814
AMA Budak H, Tunç T. Generalized Hermite-Hadamard type inequalities for products of co-ordinated convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):863-879. doi:10.31801/cfsuasmas.600814
Chicago Budak, Hüseyin, and Tuba Tunç. “Generalized Hermite-Hadamard Type Inequalities for Products of Co-Ordinated Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 863-79. https://doi.org/10.31801/cfsuasmas.600814.
EndNote Budak H, Tunç T (June 1, 2020) Generalized Hermite-Hadamard type inequalities for products of co-ordinated convex functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 863–879.
IEEE H. Budak and T. Tunç, “Generalized Hermite-Hadamard type inequalities for products of co-ordinated convex functions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 863–879, 2020, doi: 10.31801/cfsuasmas.600814.
ISNAD Budak, Hüseyin - Tunç, Tuba. “Generalized Hermite-Hadamard Type Inequalities for Products of Co-Ordinated Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 863-879. https://doi.org/10.31801/cfsuasmas.600814.
JAMA Budak H, Tunç T. Generalized Hermite-Hadamard type inequalities for products of co-ordinated convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:863–879.
MLA Budak, Hüseyin and Tuba Tunç. “Generalized Hermite-Hadamard Type Inequalities for Products of Co-Ordinated Convex Functions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 863-79, doi:10.31801/cfsuasmas.600814.
Vancouver Budak H, Tunç T. Generalized Hermite-Hadamard type inequalities for products of co-ordinated convex functions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):863-79.

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