In this paper, approximate lower and upper Hermite--Hadamard type
inequalities are obtained for functions that are approximately convex with
respect to a given Chebyshev system
In this paper, the connection between the functional inequalities f(2x+y)≤2f(x)+f(y)+αJ(x−y)(x,y∈D) and ∫01f(tx+(1−t)y)ρ(t)dt≤λf(x)+(1−λ)f(y)+αH(x−y)(x,y∈D) is investigated, where
D is a convex subset of a linear space, f:D→R,
αH,αJ:D−D→R are even functions, λ∈[0,1], and
ρ:[0,1]→R+ is an integrable nonnegative function with
∫01ρ(t)dt=1