In this paper, we investigate n-exponential convexity and log-convexity using the positive functional defined as the difference of the left-hand side and right-hand side of the inequality from (Pečarić and Janić in Facta Univ., Ser. Math. Inform. 3:39-42, ). We also give mean value theorems of Lagrange and Cauchy types. Finally, we construct means with Stolarsky property. [ABSTRACT FROM AUTHOR]
This research investigates bounds of the sum of left-sided and right-sided fractional integrals in a compact form. These bounds are established by using (α , m) -convex functions. The results of this paper also have connection with some known and already published results (Dragomir and Agarwal in Appl. Math. Lett. 11(5):91–95, 1998; Farid in J. Anal. 2018, https://doi.org/10.1007/s41478-0079-4; Farid et al. in Mathematics 2018(6):248, 2018). Moreover, the investigated results are applied to the end points as well as the mid point of the domain and some interesting consequences have been obtained. [ABSTRACT FROM AUTHOR]