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

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

Анотація

UDC 517.5

Дробовi нерiвностi типу трапецiї з узагальненими вiдносно напiв-$(m, h_1, h_2)$-преiнвексними вiдображеннями на $m$ -iнвекснiй множинi

Встановлено дробову інтегральну рівність для двічі диференційовних відображень на $m$-інвексній множині. За допомогою цієї рівності отримано нові оцінки для узагальнених нерівностей типу трапеції для відображень, у яких похідні другого порядку є узагальненими відносно напів-$(m,h_{1},h_{2})$-преінвексними через дробові інтеграли. Також обговорено деякі нові спеціальні випадки, що випливають з отриманих результатів.

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