量子积分的Ostrowski型不等式

Ostrowski type inequalities for quantum

针对一阶q导数有界的函数,利用q微积分平均值不等式,建立了q-Ostrowski不等式,加强了已有文献给出的q-Ostrowski不等式,并将结果移植到qb积分。针对一阶q导数和一阶qb导数都有界的函数,利用q微积分平均值不等式,建立了同时涉及q积分和qb积分的Ostrowski型不等式,推广了经典的Ostrowski不等式。针对二阶q可微且二阶qb可微的函数,利用恒等式,通过引入参数求最值,建立了同时涉及q积分和qb积分的Ostrowski型不等式。

In this paper,q-Ostrowski inequality is established for functions with bounded first order q-derivatives by means of mean value inequality for q-calculus,which strengthens q-Ostrowski inequality given in previous literature,and the result is transferred to qb-integral.Ostrowski inequality involving both q-integral and qb-integral is established for functions with bounded first order q-derivatives and qb-derivatives,and the classical Ostrowski inequality is generalized.For second order q-differentiable and second order qb-differentiable functions,using the identities and the method of introducing parameter to find the minimum,Ostrowski type inequality involving both q-integral and qb-integral is established.