About Aczél Inequality and Some Bounds for Several Statistical Indicators

In this paper, we will study a refinement of the Cauchy&ndash

Calculus for the intermediate point associated with a mean value theorem of the integral calculus

Abstract If f, g: [a, b] → 𝕉 are two continuous functions, then there exists a point c ∈ (a, b) such that ∫ a c f ( x ) d x + ( c - a ) g ( c ) = ∫ c b g ( x ) d x + ( b - c ) f ( c ) . \int_a^c {f\left(x \right)} dx + \left({c - a} \right)g\left(c \right) = \int_c^b {g\left(x \right)} dx + \left({b - c} \right)f\left(c \right). In this paper, we study the approaching of the point c towards a, when b approaches a.

Certain positive linear operators with better approximation properties

Properties of the intermediate point from a mean value theorem of the integral calculus - II

Abstract In this paper we consider two continuous functions f, g : [a, b] → ℝ and we study for these ones, under which circumstances the intermediate point function is four order di erentiable at the point x = a and we calculate its derivative.