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In this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained. [ABSTRACT FROM AUTHOR]

In the article, we introduce a class of n-polynomial harmonically convex functions, establish their several new Hermite–Hadamard type inequalities which are the generalizations and variants of the previously known results for harmonically convex functions. [ABSTRACT FROM AUTHOR]

We first establish some results involving Riemann–Liouville fractional integrals for partially differentiable functions. Then we obtain some fractional Ostrowski type inequalities for functions in class of functions L p , L ∞ and L 1 , respectively. We also give some midpoint type inequalities as special cases of our main results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a new extension of convexity called σ-convexity. We show that the class of σ-convex functions includes several other classes of convex functions. Some new integral inequalities of Hermite–Hadamard type are established to illustrate the applications of σ-convex functions. [ABSTRACT FROM AUTHOR]