Research Article
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Year 2022, , 775 - 786, 01.06.2022
https://doi.org/10.15672/hujms.946069

Abstract

References

  • [1] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279, 57–66, 2015.
  • [2] P. Agarwal, S.S. Dragomir, M. Jleli and B. Samet, Advances in mathematical inequalities and applications, Trends in Mathematics. Birkhäuser/Springer, Singapore, 2018.
  • [3] F.M. Atıcı and H. Yaldız, Convex functions on discrete time domains, Canad. Math. Bull. 59 (2), 225–233, 2016.
  • [4] J. Barić, R. Bibi, M. Bohner, A. Nosheen and J. Pečarić, Jensen inequalities on time scales, volume 9 of Monographs in Inequalities, ELEMENT, Zagreb, 2015.
  • [5] J. Barić, R. Bibi, M. Bohner and J. Pečarić, Time scales integral inequalities for superquadratic functions, J. Korean Math. Soc. 50 (3), 465–477, 2013.
  • [6] K.S. Chiu and T. Li, Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments, Math. Nachr. 292 (10), 2153–2164, 2019.
  • [7] P. Ciatti, M.G. Cowling and F. Ricci, Hardy and uncertainty inequalities on stratified Lie groups, Adv. Math. 277, 365–387, 2015.
  • [8] H. Gunawan and Eridani, Fractional integrals and generalized Olsen inequalities, Kyungpook Math. J. 49 (1), 31–39, 2009.
  • [9] M.A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80 (2), 545–550, 1981.
  • [10] M. Iqbal, M.I. Bhatti and K. Nazeer, Generalization of inequalities analogous to Hermite-Hadamard inequality via fractional integrals, Bull. Korean Math. Soc. 52 (3), 707–716, 2015.
  • [11] H. Kalsoom, M.A. Ali, M. Idrees, P. Agarwal and M. Arif, New post quantum analogues of Hermite-Hadamard type inequalities for interval-valued convex functions, Math. Probl. Eng. Art. ID 5529650, 17 pages, 2021.
  • [12] M.A. Khan, T. Ali, S.S. Dragomir and M.Z. Sarikaya, Hermite-Hadamard type inequalities for conformable fractional integrals, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 112 (4),1033–1048, 2018.
  • [13] U.S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput. 147 (1), 137– 146, 2004.
  • [14] T. Li, N. Pintus and G. Viglialoro, Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys. 70 (3), No. 86, 18, 2019.
  • [15] T. Li and G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime, Differential Integral Equations, 34 (5-6), 315–336, 2021.
  • [16] K. Mehrez and P. Agarwal, New Hermite-Hadamard type integral inequalities for convex functions and their applications, J. Comput. Appl. Math. 350, 274–285, 2019.
  • [17] P.O. Mohammed, Hermite-Hadamard inequalities for Riemann-Liouville fractional integrals of a convex function with respect to a monotone function, Math. Methods Appl. Sci. 44 (3), 2314–2324, 2021.
  • [18] P.O. Mohammed and T. Abdeljawad, Modification of certain fractional integral inequalities for convex functions, Adv. Difference Equ. 2020, 69, 2020.
  • [19] P.O. Mohammed, T. Abdeljawad, D. Baleanu, A. Kashuri, F. Hamasalh and P. Agarwal, New fractional inequalities of Hermite-Hadamard type involving the incomplete gamma functions, J. Inequal. Appl. 263, 1–16, 2020.
  • [20] P.O. Mohammed and F.K. Hamasalh, New conformable fractional integral inequalities of Hermite-Hadamard type for convex functions, Symmetry, 11 (2), 2019.
  • [21] P.O. Mohammed and M.Z. Sarikaya, Hermite-Hadamard type inequalities for F-convex function involving fractional integrals, J. Inequal. Appl. 359, 1–33, 2018.
  • [22] P.O. Mohammed and M.Z. Sarikaya, On generalized fractional integral inequalities for twice differentiable convex functions, J. Comput. Appl. Math. 372, 112740, 15, 2020.
  • [23] P.O. Mohammed, M.Z. Sarikaya and D. Baleanu, On the generalized Hermite- Hadamard inequalities via the tempered fractional integrals, Symmetry 12 (4), 2020.
  • [24] F. Qi, P.O. Mohammed, J.C. Yao and Y.H. Yao, Generalized fractional integral inequalities of Hermite-Hadamard type for $(\alpha,m)$-convex functions, J. Inequal. Appl. 135, 1–17, 2019.
  • [25] M. Ruzhansky, Y.J. Cho, P. Agarwal and I. Area, eds, Advances in real and complex analysis with applications, Trends in Mathematics. Birkhäuser/Springer, Singapore, 2017.
  • [26] M.Z. Sarikaya and H. Yildirim, On Hermite-Hadamard type inequalities for Riemann- Liouville fractional integrals, Miskolc Math. Notes, 17 (2), 1049–1059, 2016.
  • [27] G.N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1995.
  • [28] H. Yaldız and P. Agarwal, s-convex functions on discrete time domains, Analysis, 37 (4), 179–184, 2017.
  • [29] X.X. You, M.A. Ali, H. Budak, P. Agarwal and Y.M. Chu, Extensions of Hermite- Hadamard inequalities for harmonically convex functions via generalized fractional integrals, J. Inequal. Appl. 102, 1–22, 2021.

Hermite-Hadamard-type inequalities for conformable integrals

Year 2022, , 775 - 786, 01.06.2022
https://doi.org/10.15672/hujms.946069

Abstract

In this study, some inequalities of Hermite-Hadamard type for integrals arising in conformable fractional calculus are presented. In fact, the obtained inequalities are not only valid for those integrals arising in conformable fractional calculus, but for more general integrals as well. Numerous known versions are recovered as special cases. We also illustrate our findings via applications to modified Bessel functions, special means, and midpoint approximations.

References

  • [1] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279, 57–66, 2015.
  • [2] P. Agarwal, S.S. Dragomir, M. Jleli and B. Samet, Advances in mathematical inequalities and applications, Trends in Mathematics. Birkhäuser/Springer, Singapore, 2018.
  • [3] F.M. Atıcı and H. Yaldız, Convex functions on discrete time domains, Canad. Math. Bull. 59 (2), 225–233, 2016.
  • [4] J. Barić, R. Bibi, M. Bohner, A. Nosheen and J. Pečarić, Jensen inequalities on time scales, volume 9 of Monographs in Inequalities, ELEMENT, Zagreb, 2015.
  • [5] J. Barić, R. Bibi, M. Bohner and J. Pečarić, Time scales integral inequalities for superquadratic functions, J. Korean Math. Soc. 50 (3), 465–477, 2013.
  • [6] K.S. Chiu and T. Li, Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments, Math. Nachr. 292 (10), 2153–2164, 2019.
  • [7] P. Ciatti, M.G. Cowling and F. Ricci, Hardy and uncertainty inequalities on stratified Lie groups, Adv. Math. 277, 365–387, 2015.
  • [8] H. Gunawan and Eridani, Fractional integrals and generalized Olsen inequalities, Kyungpook Math. J. 49 (1), 31–39, 2009.
  • [9] M.A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80 (2), 545–550, 1981.
  • [10] M. Iqbal, M.I. Bhatti and K. Nazeer, Generalization of inequalities analogous to Hermite-Hadamard inequality via fractional integrals, Bull. Korean Math. Soc. 52 (3), 707–716, 2015.
  • [11] H. Kalsoom, M.A. Ali, M. Idrees, P. Agarwal and M. Arif, New post quantum analogues of Hermite-Hadamard type inequalities for interval-valued convex functions, Math. Probl. Eng. Art. ID 5529650, 17 pages, 2021.
  • [12] M.A. Khan, T. Ali, S.S. Dragomir and M.Z. Sarikaya, Hermite-Hadamard type inequalities for conformable fractional integrals, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 112 (4),1033–1048, 2018.
  • [13] U.S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput. 147 (1), 137– 146, 2004.
  • [14] T. Li, N. Pintus and G. Viglialoro, Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys. 70 (3), No. 86, 18, 2019.
  • [15] T. Li and G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime, Differential Integral Equations, 34 (5-6), 315–336, 2021.
  • [16] K. Mehrez and P. Agarwal, New Hermite-Hadamard type integral inequalities for convex functions and their applications, J. Comput. Appl. Math. 350, 274–285, 2019.
  • [17] P.O. Mohammed, Hermite-Hadamard inequalities for Riemann-Liouville fractional integrals of a convex function with respect to a monotone function, Math. Methods Appl. Sci. 44 (3), 2314–2324, 2021.
  • [18] P.O. Mohammed and T. Abdeljawad, Modification of certain fractional integral inequalities for convex functions, Adv. Difference Equ. 2020, 69, 2020.
  • [19] P.O. Mohammed, T. Abdeljawad, D. Baleanu, A. Kashuri, F. Hamasalh and P. Agarwal, New fractional inequalities of Hermite-Hadamard type involving the incomplete gamma functions, J. Inequal. Appl. 263, 1–16, 2020.
  • [20] P.O. Mohammed and F.K. Hamasalh, New conformable fractional integral inequalities of Hermite-Hadamard type for convex functions, Symmetry, 11 (2), 2019.
  • [21] P.O. Mohammed and M.Z. Sarikaya, Hermite-Hadamard type inequalities for F-convex function involving fractional integrals, J. Inequal. Appl. 359, 1–33, 2018.
  • [22] P.O. Mohammed and M.Z. Sarikaya, On generalized fractional integral inequalities for twice differentiable convex functions, J. Comput. Appl. Math. 372, 112740, 15, 2020.
  • [23] P.O. Mohammed, M.Z. Sarikaya and D. Baleanu, On the generalized Hermite- Hadamard inequalities via the tempered fractional integrals, Symmetry 12 (4), 2020.
  • [24] F. Qi, P.O. Mohammed, J.C. Yao and Y.H. Yao, Generalized fractional integral inequalities of Hermite-Hadamard type for $(\alpha,m)$-convex functions, J. Inequal. Appl. 135, 1–17, 2019.
  • [25] M. Ruzhansky, Y.J. Cho, P. Agarwal and I. Area, eds, Advances in real and complex analysis with applications, Trends in Mathematics. Birkhäuser/Springer, Singapore, 2017.
  • [26] M.Z. Sarikaya and H. Yildirim, On Hermite-Hadamard type inequalities for Riemann- Liouville fractional integrals, Miskolc Math. Notes, 17 (2), 1049–1059, 2016.
  • [27] G.N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1995.
  • [28] H. Yaldız and P. Agarwal, s-convex functions on discrete time domains, Analysis, 37 (4), 179–184, 2017.
  • [29] X.X. You, M.A. Ali, H. Budak, P. Agarwal and Y.M. Chu, Extensions of Hermite- Hadamard inequalities for harmonically convex functions via generalized fractional integrals, J. Inequal. Appl. 102, 1–22, 2021.
There are 29 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Martin Bohner 0000-0001-8310-0266

Artion Kashuri 0000-0003-0115-3079

Pshtiwan Mohammed 0000-0001-6837-8075

Juan Eduardo Napoles Valdes 0000-0003-2470-1090

Publication Date June 1, 2022
Published in Issue Year 2022

Cite

APA Bohner, M., Kashuri, A., Mohammed, P., Napoles Valdes, J. E. (2022). Hermite-Hadamard-type inequalities for conformable integrals. Hacettepe Journal of Mathematics and Statistics, 51(3), 775-786. https://doi.org/10.15672/hujms.946069
AMA Bohner M, Kashuri A, Mohammed P, Napoles Valdes JE. Hermite-Hadamard-type inequalities for conformable integrals. Hacettepe Journal of Mathematics and Statistics. June 2022;51(3):775-786. doi:10.15672/hujms.946069
Chicago Bohner, Martin, Artion Kashuri, Pshtiwan Mohammed, and Juan Eduardo Napoles Valdes. “Hermite-Hadamard-Type Inequalities for Conformable Integrals”. Hacettepe Journal of Mathematics and Statistics 51, no. 3 (June 2022): 775-86. https://doi.org/10.15672/hujms.946069.
EndNote Bohner M, Kashuri A, Mohammed P, Napoles Valdes JE (June 1, 2022) Hermite-Hadamard-type inequalities for conformable integrals. Hacettepe Journal of Mathematics and Statistics 51 3 775–786.
IEEE M. Bohner, A. Kashuri, P. Mohammed, and J. E. Napoles Valdes, “Hermite-Hadamard-type inequalities for conformable integrals”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 3, pp. 775–786, 2022, doi: 10.15672/hujms.946069.
ISNAD Bohner, Martin et al. “Hermite-Hadamard-Type Inequalities for Conformable Integrals”. Hacettepe Journal of Mathematics and Statistics 51/3 (June 2022), 775-786. https://doi.org/10.15672/hujms.946069.
JAMA Bohner M, Kashuri A, Mohammed P, Napoles Valdes JE. Hermite-Hadamard-type inequalities for conformable integrals. Hacettepe Journal of Mathematics and Statistics. 2022;51:775–786.
MLA Bohner, Martin et al. “Hermite-Hadamard-Type Inequalities for Conformable Integrals”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 3, 2022, pp. 775-86, doi:10.15672/hujms.946069.
Vancouver Bohner M, Kashuri A, Mohammed P, Napoles Valdes JE. Hermite-Hadamard-type inequalities for conformable integrals. Hacettepe Journal of Mathematics and Statistics. 2022;51(3):775-86.