Geodesic
$k-$Fractional Ostrowski Type Inequalities VIA $(s,r)-$Convex
Kragujevac Journal of Mathematics, Tome 49 (2025) no. 4, p. 527

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We introduce the generalized class named it the class of $(s,r)-$convex in mixed kind, this class includes $s-$convex in $1^{\text{st}}$ and $2^{\text{nd}}$ kind, $P-$convex, quasi convex and the class of ordinary convex. Also, we state the generalization of the classical Ostrowski inequality via $k-$fractional integrals, which is obtained for functions whose first derivative in absolute values is $(s,r)-$convex in mixed kind. Moreover, we establish some Ostrowski type inequalities via $k-$fractional integrals and their particular cases for the class of functions whose absolute values at certain powers of derivatives are $(s,r)-$convex in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means are given.
Classification : 26A33, 26A51, 26D15, 26D99, 47A30, 33B10
Keywords: Ostrowski inequality, convex function, power mean inequality, Hölder's inequality 
Ali Hassan; Asif R. Khan. $k-$Fractional Ostrowski Type Inequalities VIA $(s,r)-$Convex. Kragujevac Journal of Mathematics, Tome 49 (2025) no. 4, p. 527 . http://geodesic.mathdoc.fr/item/KJM_2025_49_4_a2/
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     author = {Ali Hassan and Asif R. Khan},
     title = {$k-${Fractional} {Ostrowski} {Type} {Inequalities} {VIA} $(s,r)-${Convex}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {527 },
     year = {2025},
     volume = {49},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2025_49_4_a2/}
}
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