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In this paper, we establish some reversed dynamic inequalities of Hilbert type on time scales nabla calculus by applying reversed Hölder's inequality, chain rule on time scales, and the mean inequality. As particular cases of our results (when T = N and T = R ), we get the reversed form of discrete and continuous inequalities proved by Chang-Jian, Lian-Ying and Cheung (Math. Slovaca 61(1):15–28, 2011). [ABSTRACT FROM AUTHOR]

Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field. [ABSTRACT FROM AUTHOR]

In this paper, we establish inequalities of Hermite–Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained results (İşcan in Hacet. J. Math. Stat. 43(6):935–942, 2014 and İşcan and Wu in Appl. Math. Comput. 238:237–244, 2014). We also discuss some special cases for our main results and obtain new inequalities of Hermite–Hadamard type. [ABSTRACT FROM AUTHOR]

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]