In this paper, we establish some generalizations of weighted trapezoid inequality for mappings of bounded variation, and give several applications for r − moment, the expectation of a continuous random variable and the Beta mapping.

Utilising the Beesack version of the Darst-Pollard inequality, some error bounds for approximating the Riemann-Stieltjes integral are given. Some applications related to the trapezoid and mid-point quadrature rules are provided.

Abstract In this paper, we offer a new quantum integral identity, the result is then used to obtain some estimates of Hermite–Hadamard inequalities for integrals. The results presented in paper are generalizations comparable literature on inequalities. Several inequalities, such as midpoint-like inequality, Simpson-like averaged midpoint–trapezoid-like and trapezoid-like obtained special cases ...

This paper derives some equalities via twice differentiable functions and conformable fractional integrals. With the help of obtained identities, we present new trapezoid-type midpoint-type inequalities convex in context New are by taking advantage convexity property, power mean inequality, Hölder’s inequality. We show that this family generalizes previous research studies special choices. Furt...

Abstract In this paper, we establish a new variant of q -Hermite-Hadamard inequality for convex functions via left and right -integrals. Moreover, prove some -midpoint -trapezoid type inequalities -differentiable functions. To illustrate the newly established inequalities, give particular examples

This paper establishes an identity for the case of differentiable $s-$convex functions with respect to conformable fractional integrals. By using this identity, sundry trapezoid-type inequalities are proven by help Several important acquired taking advantage convexity, Hölder inequality, and power mean inequality. Moreover, example graph is given in order show that our main results correct. spe...

In this paper, we generalize Cerone’s results, and a unified treatment of error estimates for a general inequality satisfying f (n−1) being of bounded variation is presented. We derive the estimates for the remainder terms of the mid-point, trapezoid, and Simpson formulas. All constants of the errors are sharp. Applications in numerical integration are also given. c © 2007 Elsevier Ltd. All rig...

Integration with weight functions is used in countless mathematical problems such as: approximation theory and spectral analysis, statistical analysis and the theory of distributions. The aim of this paper is to establish a new inequality using weight function which generalizes the inequalities of Barnett et al. in 2001 and Rafiq et al. in 2006. We also discuss some other interesting inequaliti...

In this paper, we extend some estimates of a Hermite-Hadamard type inequality for functions whose absolute values the first derivatives are $p$-convex. By means obtained inequalities, bound involving beta and hypergeometric derived as applications. Also, suggest an upper error in numerical integration $p$-convex via composite trapezoid rule.