On weighted Ostrowski type, Trapezoid type, Grüss type and Ostrowski–Grüss like inequalities on time scales

Abstract

In this paper, we first derive a weighted Montgomery identity on time scales and then establish weighted Ostrowski-type, Trapezoid-type, Grüss-type and Ostrowski–Grüss-like inequalities on time scales, respectively. These results not only provide a generalization of the known results, but also give some other interesting inequalities on time scales as special cases.

Keywords:

• Montgomery identity
• Ostrowski-type inequality
• Trapezoid-type inequality
• Grüss-type inequality
• Ostrowski–Grüss-like inequality
• time scales

AMS Subject Classifications:

• Primary 26D15
• 26E70

Acknowledgments

This work was sponsored by Qing Lan Project of Jiangsu Province, and was supported by the National Natural Science Foundation of China (Grant No. 41174165), the Tianyuan Fund of Mathematics (Grant No. 11126289) and the Teaching Research Project of NUIST (Grant No. 12JY052).