Research Article
PDF EndNote BibTex RIS Cite

A Note on Fractional Midpoint Type Inequalities for Co-ordinated (s1, s2)-Convex Functions

Year 2022, Volume 43, Issue 3, 477 - 491, 30.09.2022
https://doi.org/10.17776/csj.1088703

Abstract

In the present paper, some Hermite-Hadamard type inequalities in the case of differentiable co-ordinated (s_1," " s_2)-convex functions are investigated. Namely, the generalizations of the midpoint type inequalities in the case of differentiable co-ordinated (s_1," " s_2)-convex functions in the second sense on the rectangle from the plain are established. In addition to this, it is presented several inequalities to the case of Riemann-Liouville fractional integrals and k-Riemann-Liouville fractional integrals by choosing the special cases of our obtained main results

References

  • [1] 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 (5) (1998) 91-95.
  • [2] Kirmaci U.S., Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comput., 147 (5) (2004) 137-146.
  • [3] Iqbal M., Bhatti M.I., Nazeer K., Generalization of inequalities analogous to Hermite-Hadamard inequality via fractional integrals, Bull. Korean Math. Soc., 52 (3) (2015) 707-716.
  • [4] Dragomir S.S., On Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J Math., 4 (2001) 775-788.
  • [5] Latif M.A., Dragomir S.S., On some new inequalities for differentiable co-ordinated convex functions, J. Ineq ual. Appl., 2012 (1) (2012) 1-13.
  • [6] Sarikaya M.Z., Set E., Ozdemir M. E., Dragomir S.S., New some Hadamard's type inequalities for coordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28 (2) (2012) 137-152.
  • [7] Tunç T., Sarikaya M.Z., Yaldiz H., Fractional Hermite-Hadamard's type inequality for co-ordinated convex functions, TWMS J. Pure Appl. Math., 11 (1) (2020) 3-29.
  • [8] Sarikaya M.Z., Ertugral F., On the generalized Hermite-Hadamard inequalities, Annals of the University of Craiova, Mathematics and Computer Science Series, 47 (1) (2020) 193-213.
  • [9] Turkay M.E., Sarikaya M.Z., Budak H., Yildirim H., Some Hermite-Hadamard type inequalities for co-ordinated convex functions via generalized fractional integrals, Journal of Applied Mathematics and Computing with application, 2 (1) (2021) 1-21.
  • [10] Budak H., Hezenci F., Kara H., On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals, Adv. Difference Equ., 2021 (1) (2021) 1-32.
  • [11] Chen F., A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates, J. Math. Inequal., 8 (4) (2014) 915-923.
  • [12] Ozdemir M.E., Yildiz C., Akdemir A.O., On some new Hadamard-type inequalities for co-ordinated quasi-convex functions, Hacet. J. Math. Stat., 41 (5) (2012) 697-707.
  • [13] Latif M.A., Alomari M., On the Hadamard-type inequalities for h-convex functions on the co-ordinates, Int. J. of Math. Anal., 3 (33) (2009) 1645-1656.
  • [14] Park J., On the Hermite-Hadamard-type inequalities for co-ordinated (s," " r)-convex mappings, Inter. J. of Pure and Applied Math., 74 (2) (2012) 251-263.
  • [15] Budak H., Kara, H., Kapucu R., New midpoint type inequalities for generalized fractional integral, Computational Methods for Differential Equations, 10 (1) (2022) 93-108.
  • [16] Budak H., Pehlivan E., Kösem P., On new extensions of Hermite-Hadamard inequalities for generalized fractional integrals, Sahand Communications in Mathematical Analysis, 18 (1) (2021) 73-88.
  • [17] Han J., Mohammed P.O., Zeng H., Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function, Open Math., 18 (1) (2020) 794-806.
  • [18] Qi F., Mohammed P. O., Yao J.C., Yao Y.H., Generalized fractional integral inequalities of Hermite--Hadamard type for (α," " m)-convex functions, J Inequal Appl, 2019 (135) (2019).
  • [19] Zhao D., Ali M.A., Kashuri A., Budak H., Sarikaya M.Z., Hermite--Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals, J. Inequal. Appl., 2020 (1) 1-38.
  • [20] Agarwal, P., Dragomir, S.S., Jleli, M., Samet, B., Advances in athematical inequalities and applications, Springer Singapore, 2018.
  • [21] Agarwal, P., Vivas-Cortez, M., Rangel-Oliveros, Y., Ali, M.A., New Ostrowski type inequalities for generalized s-convex functions with applications to some special means of real numbers and to midpoint formula, AIMS Mathematics, 7 (1) (2022) 1429-1444.
  • [22] Budak H., Agarwal, P., New generalized midpoint type inequalities for fractional integral, Miskolc Math. Notes, 20 (2) (2019) 781-793.
  • [23] Butt, S.I., Umar, M., Rashid, S., Akdemir, A.O., Chu, Y.M., New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals, Adv. Difference Equ., 2020 (1) (2020) 1-24.
  • [24] Butt, S.I., Nadeem, M., Farid, G., On Caputo fractional derivatives via exponential s-convex functions, Turkish Journal of Science, 5 (2) (2020) 140-146.
  • [25] Ekinci, A., Özdemir, M.E., Set, E., New integral inequalities of Ostrowski type for quasi-convex functions with applications, Turkish Journal of Science, 5 (3) (2020) 290-304.
  • [26] Ekinci, A. Ozdemir, M., Some new integral inequalities via Riemann-Liouville integral operators, Appl. Comput. Math., 18 (3) (2019) 288-295.
  • [27] Kızıl, Ş. Avcı Ardıç, M., Inequalities for strongly convex functions via Atangana-Baleanu Integral Operators, Turkish Journal of Science, 6 (2) (2021) 96-109.
  • [28] Mohammed, P.O., Abdeljawad, T., Alqudah, M.A., Jarad, F., New discrete inequalities of Hermite–Hadamard type for convex functions, Adv. Difference Equ., 2021 (1) (2021) 1-10.
  • [29] Neang, P., Nonlaopon, K., Tariboon, J., Ntouyas, S.K., Agarwal, P., Some trapezoid and midpoint type inequalities via fractional (p,q)-calculus, Adv. Difference Equ., 2021 (1) (2021) 1-22.
  • [30] 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, J. Inequal. Appl., 2012 (1) (2012) 1-13.
  • [31] Sitthiwirattham, T., Murtaza, G., Ali, M.A., Promsakon, C., Sial, I. B., Agarwal, P., Post-quantum midpoint-type inequalities associated with twice-differentiable functions, Axioms, 11 (2) (2022) 46.
  • [32] Kara H., Budak H., Hezenci F., On Midpoint Type Inequalities for Co-Ordinated Convex Functions via Generalized Fractional Integrals, 7th Int. Ifs And Contemporary Mathematcs Conference, conference proceeding book, (2021) 133-148.

Year 2022, Volume 43, Issue 3, 477 - 491, 30.09.2022
https://doi.org/10.17776/csj.1088703

Abstract

References

  • [1] 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 (5) (1998) 91-95.
  • [2] Kirmaci U.S., Inequalities for differentiable mappings and applications to special means of real numbers to midpoint formula, Appl. Math. Comput., 147 (5) (2004) 137-146.
  • [3] Iqbal M., Bhatti M.I., Nazeer K., Generalization of inequalities analogous to Hermite-Hadamard inequality via fractional integrals, Bull. Korean Math. Soc., 52 (3) (2015) 707-716.
  • [4] Dragomir S.S., On Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J Math., 4 (2001) 775-788.
  • [5] Latif M.A., Dragomir S.S., On some new inequalities for differentiable co-ordinated convex functions, J. Ineq ual. Appl., 2012 (1) (2012) 1-13.
  • [6] Sarikaya M.Z., Set E., Ozdemir M. E., Dragomir S.S., New some Hadamard's type inequalities for coordinated convex functions, Tamsui Oxford Journal of Information and Mathematical Sciences, 28 (2) (2012) 137-152.
  • [7] Tunç T., Sarikaya M.Z., Yaldiz H., Fractional Hermite-Hadamard's type inequality for co-ordinated convex functions, TWMS J. Pure Appl. Math., 11 (1) (2020) 3-29.
  • [8] Sarikaya M.Z., Ertugral F., On the generalized Hermite-Hadamard inequalities, Annals of the University of Craiova, Mathematics and Computer Science Series, 47 (1) (2020) 193-213.
  • [9] Turkay M.E., Sarikaya M.Z., Budak H., Yildirim H., Some Hermite-Hadamard type inequalities for co-ordinated convex functions via generalized fractional integrals, Journal of Applied Mathematics and Computing with application, 2 (1) (2021) 1-21.
  • [10] Budak H., Hezenci F., Kara H., On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals, Adv. Difference Equ., 2021 (1) (2021) 1-32.
  • [11] Chen F., A note on the Hermite-Hadamard inequality for convex functions on the co-ordinates, J. Math. Inequal., 8 (4) (2014) 915-923.
  • [12] Ozdemir M.E., Yildiz C., Akdemir A.O., On some new Hadamard-type inequalities for co-ordinated quasi-convex functions, Hacet. J. Math. Stat., 41 (5) (2012) 697-707.
  • [13] Latif M.A., Alomari M., On the Hadamard-type inequalities for h-convex functions on the co-ordinates, Int. J. of Math. Anal., 3 (33) (2009) 1645-1656.
  • [14] Park J., On the Hermite-Hadamard-type inequalities for co-ordinated (s," " r)-convex mappings, Inter. J. of Pure and Applied Math., 74 (2) (2012) 251-263.
  • [15] Budak H., Kara, H., Kapucu R., New midpoint type inequalities for generalized fractional integral, Computational Methods for Differential Equations, 10 (1) (2022) 93-108.
  • [16] Budak H., Pehlivan E., Kösem P., On new extensions of Hermite-Hadamard inequalities for generalized fractional integrals, Sahand Communications in Mathematical Analysis, 18 (1) (2021) 73-88.
  • [17] Han J., Mohammed P.O., Zeng H., Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function, Open Math., 18 (1) (2020) 794-806.
  • [18] Qi F., Mohammed P. O., Yao J.C., Yao Y.H., Generalized fractional integral inequalities of Hermite--Hadamard type for (α," " m)-convex functions, J Inequal Appl, 2019 (135) (2019).
  • [19] Zhao D., Ali M.A., Kashuri A., Budak H., Sarikaya M.Z., Hermite--Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals, J. Inequal. Appl., 2020 (1) 1-38.
  • [20] Agarwal, P., Dragomir, S.S., Jleli, M., Samet, B., Advances in athematical inequalities and applications, Springer Singapore, 2018.
  • [21] Agarwal, P., Vivas-Cortez, M., Rangel-Oliveros, Y., Ali, M.A., New Ostrowski type inequalities for generalized s-convex functions with applications to some special means of real numbers and to midpoint formula, AIMS Mathematics, 7 (1) (2022) 1429-1444.
  • [22] Budak H., Agarwal, P., New generalized midpoint type inequalities for fractional integral, Miskolc Math. Notes, 20 (2) (2019) 781-793.
  • [23] Butt, S.I., Umar, M., Rashid, S., Akdemir, A.O., Chu, Y.M., New Hermite–Jensen–Mercer-type inequalities via k-fractional integrals, Adv. Difference Equ., 2020 (1) (2020) 1-24.
  • [24] Butt, S.I., Nadeem, M., Farid, G., On Caputo fractional derivatives via exponential s-convex functions, Turkish Journal of Science, 5 (2) (2020) 140-146.
  • [25] Ekinci, A., Özdemir, M.E., Set, E., New integral inequalities of Ostrowski type for quasi-convex functions with applications, Turkish Journal of Science, 5 (3) (2020) 290-304.
  • [26] Ekinci, A. Ozdemir, M., Some new integral inequalities via Riemann-Liouville integral operators, Appl. Comput. Math., 18 (3) (2019) 288-295.
  • [27] Kızıl, Ş. Avcı Ardıç, M., Inequalities for strongly convex functions via Atangana-Baleanu Integral Operators, Turkish Journal of Science, 6 (2) (2021) 96-109.
  • [28] Mohammed, P.O., Abdeljawad, T., Alqudah, M.A., Jarad, F., New discrete inequalities of Hermite–Hadamard type for convex functions, Adv. Difference Equ., 2021 (1) (2021) 1-10.
  • [29] Neang, P., Nonlaopon, K., Tariboon, J., Ntouyas, S.K., Agarwal, P., Some trapezoid and midpoint type inequalities via fractional (p,q)-calculus, Adv. Difference Equ., 2021 (1) (2021) 1-22.
  • [30] 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, J. Inequal. Appl., 2012 (1) (2012) 1-13.
  • [31] Sitthiwirattham, T., Murtaza, G., Ali, M.A., Promsakon, C., Sial, I. B., Agarwal, P., Post-quantum midpoint-type inequalities associated with twice-differentiable functions, Axioms, 11 (2) (2022) 46.
  • [32] Kara H., Budak H., Hezenci F., On Midpoint Type Inequalities for Co-Ordinated Convex Functions via Generalized Fractional Integrals, 7th Int. Ifs And Contemporary Mathematcs Conference, conference proceeding book, (2021) 133-148.

Details

Primary Language English
Subjects Mathematics
Journal Section Natural Sciences
Authors

Fatih HEZENCİ> (Primary Author)
DUZCE UNIVERSITY
0000-0003-1008-5856
Türkiye

Publication Date September 30, 2022
Application Date March 17, 2022
Acceptance Date August 3, 2022
Published in Issue Year 2022, Volume 43, Issue 3

Cite

APA Hezenci, F. (2022). A Note on Fractional Midpoint Type Inequalities for Co-ordinated (s1, s2)-Convex Functions . Cumhuriyet Science Journal , 43 (3) , 477-491 . DOI: 10.17776/csj.1088703