則此函數稱為第二類s-凸函數，記作 。 當 時，可輕易發現 s-凸函數變成定義域在 的一般凸函數。 由Pearce and Pečarić和Kirmaci et al.所證出的定理是計算(1.1)式的中間項和右項的差。而這篇論文的主要研究目的則是探討(1.1)式的中間項和左項的差。 The following inequalities . (1.1) which hold for all convex mappings are known in the literature as Hadamard’s inequality. We note that J. Hadamard was not the first who discovered them. As is pointed out by D.S. Mitrinović and I.B. Lačković, the inequalities (1.1) are due to C.Hermite who obtained them in 1883, ten years before J. Hadamard. Hudzik and Mailgranda considered, among others, the class of functions which are s-convex in the second sense. This class is defined in the following way: a function is said to be s-convex in the second sense if
holds for all , [0,1] and for some fixed . The class of s-convex functions in the second sense is denoted by . It is easily seen that for , s-convexity reduces to the ordinary convexity of functions defined on . The theorems which were proved by Pearce and Pečarić and Kirmaci et al. are estimating the difference between the middle and right terms in (1.1). The aim of this paper is estimating the difference between the middle and left terms in (1.1).
