Refinements of Hermite-Hadamard inequality for Fh-convex functions on time scales

Document Type : Research Paper

Authors

Research Group in Mathematics and Applications, Department of Mathematics, University of Lagos, Lagos, Nigeria

Abstract

In this paper, new improvements, refinements and extensions to show that an Fh-convex function on time scales satisfies Hermite-Hadamard inequality is given in several directions. Examples and applications are as well provided to further support the results obtained.

Keywords

[1] M. Bohner, and A. Peterson, Dynamic equations on time scales: An introduction with applications, Boston, Birkhauser, 2001.
[2] P.S. Bullen, Error estimates for some elementary quadrature rules, Univ. Beograd Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 602-633 (1978) 97–103.
[3] C. Dinu, Convex functions on time scales, Ann. Univ. Craiova, Math. Comp. Sci. Ser. 35 (2008) 87–96.
[4] C. Dinu, Hermite-Hadamard inequality on time scales, J. Inequal. Appl. 2008 (2008) Article ID 287947.
[5] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University (Amended version), 2002.
[6] B.O. Fagbemigun and A.A. Mogbademu, Hermite-Hadamard inequality for diamond-Fh-convex function on coordinates, Palestine J. Math. 9(2) (2020) 1–11.
[7] B.O. Fagbemigun, A.A. Mogbademu and J.O. Olaleru, Diamond-ϕh dynamics on time scales with an application to economics, Int. J. Non-linear Anal. Appl. 11(1) (2020) 277–290.
[8] B.O. Fagbemigun and A.A. Mogbademu, Some classes of convex functions on time scales, Facta Univ. Ser. Maths. Inform. 35(1) (2020) 11–28.
[9] B.O. Fagbemigun and A.A. Mogbademu, Inequalities on time scales via diamond-Fh integral, Adv. Inequal. Appl. 2021(2) (2021) 1–13.
[10] B.O. Fagbemigun, A.A. Mogbademu and J.O. Olaleru, Integral inequalities of Hermite-Hadamard type for a certain class of convex functions on time scales, Honam Math. J. (2021)(To Appear).
[11] A.El. Farissi, Simple proof and refinement of Hermite-Hadamard inequality, J. Math. Inequal. 4(3) (2010) 365–369.
[12] J. Hadamard, Etude sur les propri´et´ees des fonctions enti`eres et en particulier d’une fonction consid´er´ee par ´ Riemann, J. Math. Pures. Appl. 58 (1893) 171–215.
[13] S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math. 18 (1990) 18–56.
[14] M.A. Noor, Hermite-Hadamard integral inequalities for log-preinvex functions, J. Math. Anal. Approx. Theory 2 (2007) 126–131.
[15] P.O. Olanipekun, A.A. Mogbademu and S.S. Dragomir, Hermite-Hadamard type inequalities for a new class of harmonically Convex functions, Note Math. 38(1) (2018) 23–34.
[16] B.O. Omotoyinbo, A.A. Mogbademu and P.O. Olanipekun, Integral inequalities of Hermite-Hadamard type for λ − MT-convex functions, J. Math. Sci. Appl. 4(2) (2016) 14–22.
[17] J. Sandor, ´ Some integral inequalities, El. Math. 43 (1988) 177–180.
[18] Q. Sheng, M. Fadag, J. Henderson and J.M. Davis, An exploration of combined dynamic derivatives on time scales and their applications, Nonlinear Anal. Real World Appl. 7(3) (2006) 395–413.
[19] F.H. Wong, W.C. Lian, C.C. Yeh and R.L. Liang, Hermite-Hadamard’s inequality on time scales, Int. J. Artific. Life Res. 2(3) (2011) 51–58.
Volume 13, Issue 1
March 2022
Pages 2279-2292
  • Receive Date: 18 October 2021
  • Revise Date: 08 November 2021
  • Accept Date: 01 December 2021