Fractional trapezium-like inequalities involving generalized relative semi-$(m, h_1, h_2 )$-preinvex mappings on an $m$-invex set

T. S.  Du; C. Y. Luo; Z. Z. Huang; A. Kashuri

doi:10.37863/umzh.v72i12.6036

T. S. Du College Sci., China Three Gorges Univ. and Three Gorges Math. Res. Center, Yichang, China
C. Y. Luo College Sci., China Three Gorges Univ., Yichang, China
Z. Z. Huang College Sci., China Three Gorges Univ., Yichang, China
A. Kashuri University “Ismail Qemali”, Vlora, Albania

DOI: https://doi.org/10.37863/umzh.v72i12.6036

Keywords: Hermite-Hadamard’s inequality, Riemann-Liouville fractional integrals, relative semi-$(m, h_1, h_2)$-preinvex functions

Abstract

UDC 517.5

The authors derive a fractional integral equality concerning twice differentiable mappings defined on $m$-invex set. By using this identity, the authors obtain new estimates on generalization of trapezium-like inequalities for mappings whose second order derivatives are generalized relative semi-$(m, h_1, h_2)$-preinvex via fractional integrals. We also discuss some new special cases which can be deduced from our main results.

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