|
|
 |
| |
|
|
|
Novel Dynamic Inequalities of Ostrowski-Trapezoid- Gru ̈ ss-type on q-Difference Operator |
|
|
|
PP: 119-127 |
|
|
|
doi:10.18576/pfda/110108
|
|
|
|
Author(s) |
|
|
|
Ahmed A. El-Deeb,
Barakah Almarri,
|
|
|
|
Abstract |
|
|
| We prove some new extensions of the Ostrowski inequality and its companion inequalities on q- difference operator by using two parameters for functions whose second q-derivatives are bounded. In addition to improving some results achieved by using weak conditions, the inequalities proved here include some results proven in the literature that are inferred as limited cases. Our results in the continuous and discrete instances lead to the derivation of several original integral and difference inequalities. So, furthermore to these generalizations, some continuous inequalities are obtained as special cases of main work. Our results are proved by using the integration by parts formula on q-difference operator.
|
|
|
|
|
|
|
|
