几个积分不等式及其q模拟

摘要

通过建立定积分和q定积分的恒等式,给出推广的Hermite-Hadamard不等式的一个加细及其q模拟.分别在导函数有界和导函数满足M-李普希兹条件这两种情况下,建立了积分不等式.在q导数有界的情况下,建立了一个量子积分不等式.%This paper derives integral identity and definite q-integral identity, and uses them to obtain a refinement of the generalized Hermite-Hadamard inequality and its q-analogue.Integral inequalities are established for the cases when derivative function is bounded or satisfies the M-Lipschitz condition.A quantum integral inequality is established for the case when q-derivative function is bounded.