A short note on the fractional trapezium type integral inequalities

Authors

DOI:

https://doi.org/10.55059/ijm.2022.1.2/22

Keywords:

Hermite-Hadamard inequality, Riemann-Liouville Fractional integrals, Katugampola fractional integrals, $h$-Preinvex functions; ($\psi$,$h$)-Preinvex functions

Abstract

The author has examined a large number of mathematical articles that deal with the expansion of the convexity technique and its various strategies, and focusing on it, they have determine the connection that can be developed among fractional trapezium type inequalities for generalized convex function. The writer advance this direction by examining the Hermite-Hadamard inequality using h-preinvex function.

Author Biography

Muhammad Muddassar

Associate Professor

Department of Basic Sciences

References

Aslani, S.M., Delavar, R., & Vaezpour, S.M. Inequalities of Fejer type related to generalized convex functions with applications. Int. J. Anal. Appl. 16 (2018), 38-49.

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.

https://doi.org/10.22436/jnsa.009.02.32

Chen, H., & Katuggampola, U.N. Hermite-hadamard and Hermite-hadamard-Fejer type inequalities for generalized fractional integral. Journal of Mathematical Analysis and Applications, 446(2)(2017), 1247-1291.

https://doi.org/10.1016/j.jmaa.2016.09.018

Delavar, M.R., & De La Sen, M. Some generalizations of Hermite-Hadamard type inequalities. Springerplus. 5 (2016), 1-9.

https://doi.org/10.1186/s40064-016-3301-3

Grinalatt, M., & Linnainmaa, J.T. Jensen's Inequality, parameter uncertainty and multiperiod investment. Rev. Asset Pric. Stud. 1 (2011), 1-3.

https://doi.org/10.1093/rapstu/raq001

Hernandez Hernandez, J.E., & Vivas-Cortez, M.J. Hermite-Hadamard Inequalities type for Raina's Fractional integral Operator using η-Convex Functions. Revista Matematica Teoriay Aplicaciones (Univ. Nac. Costa Rica) 26 (2019), 1-19.

https://doi.org/10.15517/rmta.v26i1.36214

Jleli, M., O'Regan, D., & Samet, J. On Hermiteˆa€"Hadamard type inequalities via generalized fractional integrals.Turk J Math, 2016, 1221-1230.

https://doi.org/10.3906/mat-1507-79

Kermausuor, S., & Nwaeze, E.R. New integral inequalities of Hermite-Hadamard type via tha Katugampola fractional integrals for Strongly η-Quasiconvex functions.The Journal of Analysis, 2020.

https://doi.org/10.1007/s41478-020-00271-9

Kashuri, A., & Liko, R. Some new Hermite-Hadamard type inequalities and their applications. Stud. Sci. Math. Hung, 56 (2019), 103-142.

https://doi.org/10.1556/012.2019.56.1.1418

Liu, W., Wen, W., & Park, J. Hermite-Hadamard type inequalities for MT-convex functions via classical integrals and fractional integrals. J. Nonlinear Sci. Appl. 9 (2016), 766-777.

https://doi.org/10.22436/jnsa.009.03.05

Nicolescu, C., & Peerson, L. Convex Functions and Their Applications. A Contemporary Approach; CMS Books in Mathematics. Springer: New York, NY, USA, 2006.

https://doi.org/10.1007/0-387-31077-0_2

Noor, M.A. Some new classes of non-convex functions. Nonlinear Funct. Analy. Appl. 11 (2006), 165-171.

Omotoyinbo, O., & Mogbademu, A. Some new Hermite-Hadamard integral inequalities for convex functions. Int. J. Sci. Innov. Tech. 1 (2014), 1-12.

https://doi.org/10.1155/2014/796132

Pecari ˆA ́c, J.E., Proschan, F., & Tong, Y.L. Convex functions ,partial orderings and statistical applications. Mathematics. In Science and Engineering; Academic Press, Inc. Boston, MA, USA, 992.

Ruel, J.J., & Ayres, M.P. Jensen's inequality predicts effects of environmental variations. Trends Ecol. Evol., 14 (1999), 361-366.

https://doi.org/10.1016/S0169-5347(99)01664-X

Vivas, M., Hernandez Hernandez, J.E., & Merentes, N. New Hermite-Hadamard and Jensen type inequalities for h-convex functions on fractal sets. Rev. Colomb. Matematicas, 50 (2016), 145-164.

https://doi.org/10.15446/recolma.v50n2.62207

Vivas-Cortez, M. Fejer type inequalities for (s, m)-convex functions in second sense. Appl. Math. Inf. Sci. 10 (2016), 1689-1696.

https://doi.org/10.18576/amis/100507

Xi, B.Y., & Qi, F. Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means. J. Funct. Spaces Appl., 2012, 1-14.

https://doi.org/10.1155/2012/980438

Downloads

Published

2022-04-14

How to Cite

Muddassar, M. ., & Bibi, F. (2022). A short note on the fractional trapezium type integral inequalities. Innovative Journal of Mathematics (IJM), 1(2), 63–70. https://doi.org/10.55059/ijm.2022.1.2/22

Issue

Section

Articles