Simpson Type Inequalities for Twice-differentiable Functions Arising from Tempered Fractional Integral OperatorsJieyin CaiBin WangTingsong DuIAENG International Journal of Applied Mathematics
摘要: In this article, by using the H¨older integral inequality, power mean integral inequality and the propertie of modulus, some new upper bounds for twice differentiable functions whose q-th powers are geometrically convex and monotonically decreasing are obtained....
In this paper, by setting up an integral identity for continuously twice differentiable functions, the author obtain some new generalized integral inequalities which give an estimate between ab/b-a {upper left or lower right curly bracket section}ba f(x)/x3 dx and 1/2{f(a)/a + f(b)/b...
(1) Prove that the function f(x) = |x|^3 is twice differentiable (i.e f' and f'''exist for every real x). (2) Is f'' differentiable at 0? why? A function is defined on the interval { (\frac{- \pi}{2},\frac{...
Then, according to the Fundamental Theorem of Calculus, we have ∫abf(x)dx=F(b)−F(a). Answer and Explanation: The function f(x)=sin(πx) has this property: it is a non-constant differentiable function, and for every integer...
functions is rather broad and contains for example every twice continuously differentiable function. For an overview over d.c. functions, see e.g. [5]. The classical approach to iteratively find local extrema of d.c. problems was described by Tao and An [6] in 1997 under the name DCA (...
Answer to: (1) Prove that the function f(x) = |x|^3 is twice differentiable (i.e f' and f'''exist for every real x). (2) Is f'' differentiable at...
Park, J.: On Simpson-like type integral inequalities for differentiable preinvex functions. Appl. Math. Sci. 7(121), 6009–6021 (2013) MathSciNet Google Scholar Sarıkaya, M.Z.: On the Hermite–Hadamard-type inequalities for co-ordinated convex function via fractional integrals. Integral...
Answer to: Show that if f : [a,b] \rightarrow \mathbb{R} is differentiable and for every continuous function g , one has \int_{a}^{b} f(x)g(x)...
For continuous and differentiable functions, we can say that for every two zeros of the function we will always have a zero of the first derivative. Answer and Explanation:1 Guessing there are two values at the interval...