Open AccessSome novel inequalities involving a function’s fractional integrals in relation to another function through generalized quasiconvex mappings
Author(s) -
R Eze Nwaeze,
Artion Kashuri
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2010349n
Subject(s) - mathematics , quasiconvex function , hadamard transform , pure mathematics , function (biology) , midpoint , fractional calculus , mathematical analysis , regular polygon , convex analysis , geometry , biology , convex optimization , evolutionary biology
In this paper, we establish new inequalities of the Hermite-Hadamard, midpoint and trapezoid types for functions whose first derivatives in absolute value are ?-quasiconvex by means of generalized fractional integral operators with respect to another function ? : [?,?] ? (0,?). Our theorems reduce to results involving the Riemann-Liouville fractional integral operators if ? is the identity map, and results involving the Hadamard operators if ?(x) = ln x. More inequalities can be deduced by choosing different bifunctions for ?. To the best of our knowledge, the results obtained herein are new and we hope that they will stimulate further interest in this direction.