Inequalities For S-convex Functions Research Articles

Extensions of Ostrowski Type Inequalities via h -Integrals and s-Convexity

In this paper, Hölder, Minkowski, and power mean inequalities are used to establish Ostrowski type inequalities for s -convex functions via h -calculus. The new inequalities are generalized versions of Ostrowski type inequalities available in literature.

Integral inequalities for s-convex functions via generalized conformable fractional integral operators

We introduce new operators, the so-called left and right generalized conformable fractional integral operators. By using these operators we establish new Hermite–Hadamard inequalities for s-convex functions and products of two s-convex functions in the second sense. Also, we obtain two interesting identities for a differentiable function involving a generalized conformable fractional integral operator. By applying these identities we give Hermite–Hadamard and midpoint-type integral inequalities for s-convex functions. Different special cases have been identified and some known results are recovered from our general results. These results may motivate further research in different areas of pure and applied sciences.

Some new Hermite\u2013Hadamard type inequalities for s-convex functions and their applications

In this paper, we establish some new integral inequalities of Hermite–Hadamard type for s-convex functions by using the Hölder–İşcan integral inequality. We also compare our new results with the known results and show that the results which we obtained are better than the known results. Finally, we give some applications to trapezoidal formula and to special means.

Investigation of s-convex functions by using convex combinations

This work is inspired by the paper [7], where the authors consider m-convex functions. The main aim of this paper is to establish some inequalities for s-convex functions without using their derivatives. Also we obtain some new results in discrete form.

Some Improvements on Hermite-Hadamard's Inequalities for s-convex Functions

Using an integral identity for a once differentiable mapping, this paper es- tablishes Hadamard's integral inequalities for s-convex and s-concave mappings. In particular, our results improve and extend some known ones in the literature. Finally, these inequalities are applied to special means. AMS subject classifications: 26D15, 26A51, 26E60, 41A55

Hermite-Hadamard-Fejer type inequalities for s-convex function in the second sense via fractional integrals

In this paper, we established Hermite-Hadamard-Fejer type inequalities for s-convex functions in the second sense via fractional integrals. The some results presented here would provide extansions of those given in earlier works.

Remarks on some inequalities for s-convex functions and applications

Some new inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected.

On Hermite-Hadamard Type Inequalities fors-Convex Functions on the Coordinates via Riemann-Liouville Fractional Integrals

We obtain some Hermite-Hadamard type inequalities fors-convex functions on the coordinates via Riemann-Liouville integrals. Some integral inequalities with the right-hand side of the fractional Hermite-Hadamard type inequality are also established.

On some inequalities for s-convex functions and applications

Abstract Some new results related to the left-hand side of the Hermite-Hadamard type inequalities for the class of functions whose second derivatives at certain powers are s-convex functions in the second sense are obtained. Also, some applications to special means of real numbers are provided. MSC:26A51, 26D15.