Geodesic
Some novel inequalities involving a function's fractional integrals in relation to another function through generalized quasiconvex mappings
Filomat, Tome 34 (2020) no. 10, p. 3349

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DOI

In this paper, we establish new inequalities of the Hermite–Hadamard, midpoint and trapezoid types for functions whose first derivatives in absolute value are η-quasiconvex by means of generalized fractional integral operators with respect to another function ω : [α, β] → (0,∞). Our theorems reduce to results involving the Riemann–Liouville fractional integral operators if ω is the identity map, and results involving the Hadamard operators if ω(x) = ln x. More inequalities can be deduced by choosing different bifunctions for η. To the best of our knowledge, the results obtained herein are new and we hope that they will stimulate further interest in this direction.
DOI : 10.2298/FIL2010349N
Classification : 26A51, 26D15, 26E60, 41A55
Keywords: Hermite–Hadamard inequality, convex functions, quasiconvex functions, Riemann–Liouville operators, Hadamard fractional operators 
Eze R Nwaeze; Artion Kashuri. Some novel inequalities involving a function's fractional integrals in relation to another function through generalized quasiconvex mappings. Filomat, Tome 34 (2020) no. 10, p. 3349 . doi: 10.2298/FIL2010349N
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     title = {Some novel inequalities involving a function's fractional integrals in relation to another function through generalized quasiconvex mappings},
     journal = {Filomat},
     pages = {3349 },
     year = {2020},
     volume = {34},
     number = {10},
     doi = {10.2298/FIL2010349N},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2010349N/}
}
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