Document Type : Research Paper
Authors
1 Department of Mathematics, Govt. Graduate College Sahiwal, Pakistan.
2 Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan 60800, Pakistan.
Abstract
In this paper, for generalised preinvex functions, new estimates of the Fej'{e}r-Hermite-Hadamard inequality on fractional sets $\mathbb{R}^{\rho }$ are given in this study. We demonstrated a fractional integral inequalities based on Fej'{e}r-Hermite-Hadamard theory. We establish two new local fractional integral identities for differentiable functions. We construct several novel Fej'{e}r-Hermite-Hadamard-type inequalities for generalized convex function in local fractional calculus
contexts using these integral identities. We provide a few illustrations to highlight the uses of the obtained findings. Furthermore, we have also given a few examples of new inequalities in use.
Keywords
- Hermite-Hadamard-inequality
- Hermite-Hadamard-Fejér inequality
- Local fractional integral
- Generalized Preinvex function
Main Subjects
[7] S. Erden, M.Z. Sarikaya and N. Celik, Some generalized inequalities involving local fractional integrals and their applications for random variables and numerical integration, J. Appl. Math. Stat. Inform., 12(2) (2016) pp. 49-65.
[8] L. Fejér, Uber die Fourierreihen, II. Math. Naturwiss Anz. Ungar. Akad. Wiss., 24 (1906) pp. 369-390.
[16] T. Weir and B. Mond, Preinvex functions in multiple objective optimization, J. Math. Anal. Appl., 136(1) (1998) pp. 29-38.