Some extended trapezoid-type inequalities and applications

Authors : Kuei Lin TSENG, Shiow Ru HWANGY

Pages : 827-850

View : 14 | Download : 9

Publication Date : 2016-06-01

Article Type : Research Paper

Abstract :In this paper, we shall establish some extended trapezoid-type $$\bigg|\dfrac{c-a}{b-a}finsert ignore into journalissuearticles values(x);+\dfrac{b-c}{b-a}finsert ignore into journalissuearticles values(y);-\dfrac{1}{b-a}\int_a^bfinsert ignore into journalissuearticles values(t);dt\bigg|,\:insert ignore into journalissuearticles values(a\leq x\leq c\leq y\leq b);$$ inequalities for differentiable convex functions and differentiable concave functions which are connected with Hermite-Hadamard inequality. Some error estimates for the midpoint, trapezoidal and Ostrowski formulae are also given.
Keywords : Hermite Hadamard Inequality, Midpoint Inequality, Trapezoid Inequality, Ostrowski Inequality, Convex Function, Concave Functions, Special Means, QuadratureRules