Remarks on some inequalities for s-convex functions and applications

holds for all x, y ∈ [,∞), λ ∈ [, ] and for some fixed s ∈ (, ]. The class of s-convex functions in the second sense is usually denoted by K s . It can be easily seen that for s =  s-convexity reduces to ordinary convexity of functions defined on [,∞). It is proved in [] that all functions from K s , s ∈ (, ) are nonnegative. Similarly, a function f : [,∞)→ R is said to be s-concave in the second sense for some fixed s ∈ (, ] if –f ∈ K s . Thus we can conclude that an s-concave function is always nonpositive for any s ∈ (, ).