TY  - JOUR
T1  - Some extended trapezoid-type inequalities and applications
AU  - Hwangy, Shiow Ru
AU  - Tseng, Kuei Lin
PY  - 2016
DA  - June
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 827
EP  - 850
VL  - 45
IS  - 3
LA  - en
AB  - In this paper, we shall establish some extended trapezoid-type$$\bigg|\dfrac{c-a}{b-a}f(x)+\dfrac{b-c}{b-a}f(y)-\dfrac{1}{b-a}\int_a^bf(t)dt\bigg|,\:(a\leq x\leq c\leq y\leq b)$$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.
KW  - Hermite-Hadamard Inequality
KW  - Midpoint Inequality
KW  - Trapezoid Inequality
KW  - Ostrowski Inequality
KW  - Convex Function
KW  - Concave Functions
KW  - Special Means
KW  - QuadratureRules
CR  - .
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UR  - https://dergipark.org.tr/en/pub/hujms/article/524197
L1  - https://dergipark.org.tr/en/download/article-file/644521
ER  -