THE HADAMARD INEQUALITIES FOR s-CONVEX FUNCTIONS IN THE SECOND SENSE

Abstract

Abstract. We derive some inequalities of Hadamard's type for s-cdnvex functions in the second sense and give some applications connected with special means. IntroductionIn the paper [11] the following class of functions was considered.

Inequalities of Hermite-Hadamard Type for Composite <em>h</em>-Convex Functions

“…For some properties of this class of functions see [2], [3], [10], [11], [40], [41], [53], [55] and [67].…”

Some new fractional integral inequalities for s-convex functions

“…In [5], Dragomir and Fitzpatrick presented the Hermite-Hadamard inequalities for s-convex functions in the second sense as follows. The constant k = 1 s+1 is the best possible in the second inequality in (1.3).…”

“…The constant k = 1 s+1 is the best possible in the second inequality in (1.3). For other recent result concerning s-convex functions, see [2,5,8,16,17]. We will now give definitions of the right-hand side and left-hand side Riemann-Liouville fractional integrals which are used throughout this paper.…”

Several complementary inequalities to inequalities of Hermite-Hadamard type for s-convex functions

“…In [6], Dragomir and Fitzpatrick proved a variant of Hermite-Hadamard inequality which holds for the s-convex functions. In [8],İşcan gave definition of harmonically convexity as follows:…”